A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband's selection is \(\dfrac{1}{7}\) and that of the wife's selection is \(\dfrac{1}{5}\). If the events are independent, then the probability of which one of the following is \(\dfrac{11}{35} \ ?\)

Only one of them will be selected

At least one of them will be selected

Only one of them will be selected

If X is a Poisson random variate with mean 3, then P(|X- 3| < 1) will be:

\(\left( \dfrac{99}{8} \right) e^{-3}\)

If n1, n2 are the sizes, x̅1, x̅2 the means, σ1, σ2 the standard deviations, the variance of the combined series is (where d1 = x̅1 – x̅ and d2 = x̅2 – x̅)

\(\left( {\frac{1}{{{n_1}}} - \frac{1}{{{n_2}}}} \right)\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)

\(\left( {\frac{1}{{{n_1}}} + \frac{1}{{{n_2}}}} \right)\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)

\(\frac{1}{{{n_1} + {n_2}}}\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)

\(\left( {\frac{1}{{{n_1}}} - \frac{1}{{{n_2}}}} \right)\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)

\(\frac{1}{{{n_1} - {n_2}}}\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)

For two events A and B, which of the following relations is true?

P(A̅ ∪ B̅) = 1 - P(A ∪ B)

\(P(\bar A \cup \bar B) = 1 - P(A)P\left(\frac B A\right)\)

P(A̅ ∪ B̅) = 1 - P(A ∪ B)

\(P(\bar A \cup \bar B) = P(\overline {A\cup B})\)

P(A̅ ∪ B̅) = P(A̅) + P(B̅)

992 + Mcqs in Probability in General Aptitude Page 4 McqOptions

151.	A bag contains 10 white balls and 5 blue balls. A ball is drawn from the bag and its color is noted. This ball is put back in the bag along with 3 more balls of the same color. A ball is drawn again from the bag at random. The probability that the first ball drawn is blue, given that the second ball drawn is blue, is:
A.	1 / 3
B.	3 / 4
C.	8 / 9
D.	4 / 9
Answer» E.

152.	19 defective pens have accidentally got mixed with 361 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a defective one.
A.	1 / 20
B.	1 / 10
C.	2 / 19
D.	1 / 19
Answer» B. 1 / 10

153.	An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statements is/are correct?1. The probability that no head is observed is \(\frac{1}{{16}}\).2. The probability that the experiment ends with three tosses is \(\frac{1}{{8}}\).Select the correct answer using the code given below:
A.	1 only
B.	2 only
C.	Both 1 and 2
D.	Neither 1 nor 2
Answer» D. Neither 1 nor 2

154.	If \(\rm P(A\cup B)=\dfrac{5}{6}, P(A\cap B)=\dfrac{1}{3}\:and\:P(\bar A)=\dfrac{1}{2}\), then which of the following is/are correct?1. A and B are independent events.2. A and B are mutually exclusive events.Select the correct answer using the code given below.
A.	1 only
B.	2 only
C.	Both 1 and 2
D.	Neither 1 nor 2
Answer» B. 2 only

155.	Approximately what area is covered under the normal distribution curve between ±3 standard deviation?
A.	80%
B.	88.60%
C.	99.73%
D.	68.00%
Answer» D. 68.00%

156.	A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is not red?
A.	3/10
B.	1/5
C.	1/2
D.	4/5
Answer» D. 4/5

157.	A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband's selection is \(\dfrac{1}{7}\) and that of the wife's selection is \(\dfrac{1}{5}\). If the events are independent, then the probability of which one of the following is \(\dfrac{11}{35} \ ?\)
A.	At least one of them will be selected
B.	Only one of them will be selected
C.	None of them will be selected
D.	Both of them will be selected
Answer» B. Only one of them will be selected

158.	A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?
A.	\(\frac{1}{2}\)
B.	\(\frac{3}{8}\)
C.	\(\frac{1}{4}\)
D.	\(\frac{1}{8}\)
Answer» B. \(\frac{3}{8}\)

159.	If 3 unbiased coins are tossed simultaneously, then the probability of getting atmost one head is
A.	\(\frac{1}{8}\)
B.	\(\frac{1}{4}\)
C.	\(\frac{3}{8}\)
D.	\(\frac{1}{2}\)
Answer» E.

160.	In a shooting test, the probabilities of hitting the target are 1/2 for A, 2/3 for B and 3/4 for C. If they fire at the same target, what is the probability that only one of them hits the target?
A.	1/4
B.	2/3
C.	1/6
D.	3/8
Answer» B. 2/3

161.	A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?
A.	17
B.	16
C.	13
D.	11
Answer» C. 13

162.	A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is
A.	0.0036
B.	0.1937
C.	0.2234
D.	0.3874
Answer» C. 0.2234

163.	Five cards-the ten, jack, queen, king and ace of hearts, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the Ace?
A.	1 / 5
B.	¼
C.	4 / 5
D.	2 / 5
Answer» B. ¼

164.	A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle than to its boundary?
A.	\(\frac{1}{5}\)
B.	\(\frac{1}{4}\)
C.	\(\frac{1}{3}\)
D.	\(\frac{1}{2}\)
Answer» C. \(\frac{1}{3}\)

166.	A box contains 2 blue caps, 4 red caps, 5 greens caps and 1 yellow cap. If four caps are picked at random, the probability that none of the is green is
A.	7/99
B.	7/12
C.	5/99
D.	5/12
Answer» B. 7/12

165.	P and Q are considering to apply for a job. The probability that P applies for the job is \(\frac{1}{4}\), the probability that P applies for the job given that Q applies for the job is \(\frac{1}{2}\), and the probability that Q applies for the job given that P applies for the job is \(\frac{1}{3}\). Then the probability that P does not apply for the job given that Q does not apply for the job is
A.	\(\frac{4}{5}\)
B.	\(\frac{5}{6}\)
C.	\(\frac{7}{8}\)
D.	\(\frac{{11}}{{12}}\)
Answer» B. \(\frac{5}{6}\)

167.	A box contains red, green and blue colored balls. When one ball is drawn randomly from the box, the probability that it is either green or blue is 2/3. Also, the probability that the ball drawn randomly from the box is either red or green is 3/5. When two balls are drawn one after another from the box, the probability that both balls are of green color is 1/15. Find the total number of balls in the box.
A.	15
B.	20
C.	30
D.	45
E.	60
Answer» E. 60

168.	If X is a Poisson random variate with mean 3, then P(\|X- 3\| < 1) will be:
A.	\(\dfrac{9}{2} e^{-3}\)
B.	0.003
C.	\(\dfrac{e^{-3}}{2}\)
D.	\(\left( \dfrac{99}{8} \right) e^{-3}\)
Answer» B. 0.003

169.	A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both win a prize. The probability that they will not win a prize in a single trial is
A.	\(\frac{1}{25}\)
B.	\(\frac{24}{25}\)
C.	\(\frac{2}{25}\)
D.	\(\frac{3}{25}\)
Answer» C. \(\frac{2}{25}\)

170.	If n1, n2 are the sizes, x̅1, x̅2 the means, σ1, σ2 the standard deviations, the variance of the combined series is (where d1 = x̅1 – x̅ and d2 = x̅2 – x̅)
A.	\(\left( {\frac{1}{{{n_1}}} + \frac{1}{{{n_2}}}} \right)\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)
B.	\(\frac{1}{{{n_1} + {n_2}}}\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)
C.	\(\left( {\frac{1}{{{n_1}}} - \frac{1}{{{n_2}}}} \right)\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)
D.	\(\frac{1}{{{n_1} - {n_2}}}\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)
Answer» C. \(\left( {\frac{1}{{{n_1}}} - \frac{1}{{{n_2}}}} \right)\left( {{n_1}\left( {\sigma _1^2 + d_1^2} \right) + {n_2}\left( {\sigma _2^2 + d_2^2} \right)} \right)\)

171.	For two events A and B, which of the following relations is true?
A.	\(P(\bar A \cup \bar B) = 1 - P(A)P\left(\frac B A\right)\)
B.	P(A̅ ∪ B̅) = 1 - P(A ∪ B)
C.	\(P(\bar A \cup \bar B) = P(\overline {A\cup B})\)
D.	P(A̅ ∪ B̅) = P(A̅) + P(B̅)
Answer» B. P(A̅ ∪ B̅) = 1 - P(A ∪ B)

172.	A and B are two candidates appearing for an interview by a company. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. The probability of B getting selected is
A.	0.9
B.	≤ 0.3
C.	≤ 0.6
D.	0.5
Answer» D. 0.5

173.	8 coins are tossed simultaneously. The probability of getting at least 6 heads is
A.	7/64
B.	57/64
C.	37/256
D.	229/256
Answer» D. 229/256

174.	A coin is tossed thrice. Find the probability of getting exactly two heads.
A.	5/8
B.	1/8
C.	1/2
D.	3/8
Answer» E.

175.	Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.Quantity I: A coin is tossed 3 times. What is the probability of getting a tail each time?Quantity II: 1/16
A.	Quantity I > Quantity II
B.	Quantity I < Quantity II
C.	Quantity I ≥ Quantity II
D.	Quantity I ≤ Quantity II
E.	Quantity I = Quantity II
Answer» B. Quantity I < Quantity II

Explore topic-wise MCQs in General Aptitude.

19 defective pens have accidentally got mixed with 361 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a defective one.

If \(\rm P(A\cup B)=\dfrac{5}{6}, P(A\cap B)=\dfrac{1}{3}\:and\:P(\bar A)=\dfrac{1}{2}\), then which of the following is/are correct?1. A and B are independent events.2. A and B are mutually exclusive events.Select the correct answer using the code given below.

Approximately what area is covered under the normal distribution curve between ±3 standard deviation?

A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is not red?

A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?

If 3 unbiased coins are tossed simultaneously, then the probability of getting atmost one head is

In a shooting test, the probabilities of hitting the target are 1/2 for A, 2/3 for B and 3/4 for C. If they fire at the same target, what is the probability that only one of them hits the target?

A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is

Five cards-the ten, jack, queen, king and ace of hearts, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the Ace?

A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle than to its boundary?

A box contains 2 blue caps, 4 red caps, 5 greens caps and 1 yellow cap. If four caps are picked at random, the probability that none of the is green is

If X is a Poisson random variate with mean 3, then P(|X- 3| < 1) will be:

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both win a prize. The probability that they will not win a prize in a single trial is

If n1, n2 are the sizes, x̅1, x̅2 the means, σ1, σ2 the standard deviations, the variance of the combined series is (where d1 = x̅1 – x̅ and d2 = x̅2 – x̅)

For two events A and B, which of the following relations is true?

A and B are two candidates appearing for an interview by a company. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. The probability of B getting selected is

8 coins are tossed simultaneously. The probability of getting at least 6 heads is

A coin is tossed thrice. Find the probability of getting exactly two heads.

A bag contains 8 white, 5 black and 4 blue balls. One ball is drawn randomly, what is the probability that it is neither white nor blue ball?

A box contains 12 blue pens and 18 black pens. Two pens are taken out one after the other, without placing the other pens in their place. How likely is it that the first pen is of blue color and the second of black?

If a fair dice is rolled successively, then the probability that 1 appears in an even numbered throw is

If a single card is chosen at random from a standard deck of 52 playing cards, then the probability of choosing a black queen or a spade card is:

A dice is rolled two times. Find the probability of getting a composite number on first roll and a prime number on second roll?

In a binomial distribution, the mean is \(\frac{2}{3}\) and the variance is \(\frac{5}{9}\). What is the probability that X = 2?

A speaks the truth 3 out of 4 times, and B 5 out of 6 times, what is the probability that they will contradict each other in stating the same fact?

If P(E) = 0.07, then what is the probability of 'not E'?

A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is

A box contains 5 yellow, 4 green and 3 white marbles. If 3 marbles are drawn at random, then what is the probability that they are not of the same colour?

A dice is rolled, what is the probability of even numbered outcomes:

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement. The probability of getting exactly one red ball is

If two dices A and B are rolled simultaneously, what is the probability that the number appearing on the top faces of the dice A is a multiple of number appearing on the top faces of the dice B and vice versa?

In a lottery, 10,000 tickets are sold and ten prizes are awarded. What is the probability of not getting a prize if you buy one ticket?

On selecting a 3 digit number at random, what is the probability of selecting a number which is divisible by both 5 and 9?

A problem in statistics is given to three students A, B and C whose chances of solving it independently are \(\frac{1}{2},\frac{1}{3}\) and \(\frac{1}{4}\) respectively. The probability that the problem will be solved is

If P(E) = 0.05, what is the probability of 'not E'?

A student takes an 18 question multiple-choice exam, with four choices per question. Suppose one of the choices in obviously incorrect, and the student makes an “educated” guess of the remaining choices, then the expected number of the correct answer is

In a class of 125 students, 70 passed in Mathematics, 55 passed in Statistics and 30 passed in both. What is the probability that a student selected at random from the class has passed in only one subject?

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then \(\left( {\frac{{{\rm{\;mean\;of\;}}X}}{{{\rm{\;standard\;deviation\;of\;}}X}}} \right)\) is equal to:

A is targeting B, B and C are targeting A. Probability of hitting the target by A, B and C are \(\dfrac{2}{3}, \dfrac{1}{2}\) and \(\dfrac{1}{3}\) respectively. If A is hit then the probability that B hits the target and C does not, is

A card is drawn from a deck of cards. What is the probability that it is either a spade or an Ace or both?

On tossing three coins simultaneously then the probability of getting 3 heads, is

A pair of unbiased dice is rolled simultaneously. Find the probability of getting a difference of three.

176.	A bag contains 8 white, 5 black and 4 blue balls. One ball is drawn randomly, what is the probability that it is neither white nor blue ball?
A.	5/17
B.	8/17
C.	4/17
D.	6/17
Answer» B. 8/17

177.	A box contains 12 blue pens and 18 black pens. Two pens are taken out one after the other, without placing the other pens in their place. How likely is it that the first pen is of blue color and the second of black?
A.	18/39
B.	36/145
C.	36/125
D.	18/154
Answer» C. 36/125

178.	If a fair dice is rolled successively, then the probability that 1 appears in an even numbered throw is
A.	5 / 36
B.	6 / 11
C.	1 / 6
D.	5 / 11
Answer» E.

179.	If a single card is chosen at random from a standard deck of 52 playing cards, then the probability of choosing a black queen or a spade card is:
A.	\(\frac{7}{{26}}\)
B.	\(\frac{{17}}{{52}}\)
C.	\(\frac{4}{{13}}\)
D.	\(\frac{{15}}{{52}}\)
Answer» B. \(\frac{{17}}{{52}}\)

180.	A dice is rolled two times. Find the probability of getting a composite number on first roll and a prime number on second roll?
A.	\(\frac{1}{2}\)
B.	\(\frac{1}{6}\)
C.	\(\frac{1}{9}\)
D.	\(\frac{1}{4}\)
Answer» C. \(\frac{1}{9}\)

181.	In a binomial distribution, the mean is \(\frac{2}{3}\) and the variance is \(\frac{5}{9}\). What is the probability that X = 2?
A.	\(\frac{5}{36}\)
B.	\(\frac{25}{36}\)
C.	\(\frac{25}{216}\)
D.	\(\frac{25}{54}\)
Answer» D. \(\frac{25}{54}\)

182.	A speaks the truth 3 out of 4 times, and B 5 out of 6 times, what is the probability that they will contradict each other in stating the same fact?
A.	2/3
B.	1/3
C.	5/6
D.	1/21
Answer» C. 5/6

183.	If P(E) = 0.07, then what is the probability of 'not E'?
A.	0.93
B.	0.95
C.	0.89
D.	0.9
Answer» B. 0.95

184.	A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is
A.	4/8
B.	5/8
C.	6/8
D.	7/8
Answer» C. 6/8

185.	A box contains 5 yellow, 4 green and 3 white marbles. If 3 marbles are drawn at random, then what is the probability that they are not of the same colour?
A.	\(\frac{13}{55}\)
B.	\(\frac{41}{44}\)
C.	\(\frac{55}{13}\)
D.	\(\frac{44}{41}\)
Answer» C. \(\frac{55}{13}\)