MCQOPTIONS
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MCQOPTIONS
This section includes 29 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Bag 1 contains 4 white and 6 black balls while another Bag 2 contains 4 white and 3 black balls. One ball is drawn at random from one of the bags and it is found to be black. Find the probability that it was drawn from Bag 1. |
| A. | 12/13 |
| B. | 5/12 |
| C. | 7/11 |
| D. | 7/12 |
| Answer» E. | |
| 2. |
Bag 1 contains 3 red and 5 black balls while another Bag 2 contains 4 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it is drawn from bag 2. |
| A. | 31/62 |
| B. | 16/62 |
| C. | 16/31 |
| D. | 31/32 |
| Answer» D. 31/32 | |
| 3. |
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. |
| A. | 1/8 |
| B. | 5/8 |
| C. | 2/7 |
| D. | 3/8 |
| Answer» E. | |
| 4. |
Previous probabilities in Bayes Theorem that are changed with the new available information are called __________ |
| A. | independent probabilities |
| B. | dependent probabilities |
| C. | interior probabilities |
| D. | posterior probabilities |
| Answer» E. | |
| 5. |
Formula for conditional probability P(A|B) is _______a) P(A|B) = \(\frac{P(A∩B)}{P(B)}\) b) P(A|B) = \(\frac{P(A∩B)}{P(A)}\) c) P(A|B) = \(\frac{P(A)}{P(B)}\) d) P(A|B) = \(\frac{P(B)}{P( |
| A. | P(A|B) = \(\frac{P(A∩B)}{P(B)}\) |
| B. | P(A|B) = \(\frac{P(A∩B)}{P(A)}\) |
| C. | P(A|B) = \(\frac{P(A)}{P(B)}\) |
| D. | P(A|B) = \(\frac{P(B)}{P(A)}\) |
| Answer» B. P(A|B) = \(\frac{P(A∩B)}{P(A)}\) | |
| 6. |
Formula for Bayes theorem is ________a) P(A|B) = \(\frac{P(B│A)P(A)}{P(B)}\) b) P(A|B) = \(\frac{P(A)}{P(B)}\) c) P(A|B) = \(\frac{P(B│ |
| A. | P(A|B) = \(\frac{P(B│A)P(A)}{P(B)}\) |
| B. | P(A|B) = \(\frac{P(A)}{P(B)}\) |
| C. | P(A|B) = \(\frac{P(B│A)}{P(B)}\) |
| D. | P(A|B) = \(\frac{1}{P(B)}\) |
| Answer» B. P(A|B) = \(\frac{P(A)}{P(B)}\) | |
| 7. |
Method in which the previously calculated probabilities are revised with values of new probability is called __________ |
| A. | Revision theorem |
| B. | Bayes theorem |
| C. | Dependent theorem |
| D. | Updation theorem |
| Answer» C. Dependent theorem | |
| 8. |
A bucket contains 6 blue, 8 red and 9 black pens. If six pens are drawn one by one without replacement, find the probability of getting all black pens? |
| A. | \(\frac{8}{213}\) |
| B. | \(\frac{8}{4807}\) |
| C. | \(\frac{5}{1204}\) |
| D. | \(\frac{7}{4328}\) |
| Answer» C. \(\frac{5}{1204}\) | |
| 9. |
A bin contains 4 red and 6 blue balls and three balls are drawn at random. Find the probability such that both are of the same color. |
| A. | \(\frac{10}{28}\) |
| B. | \(\frac{1}{5}\) |
| C. | \(\frac{1}{10}\) |
| D. | \(\frac{4}{7}\) |
| Answer» C. \(\frac{1}{10}\) | |
| 10. |
A jar containing 8 marbles of which 4 red and 4 blue marbles are there. Find the probability of getting a red given the first one was red too. |
| A. | \(\frac{4}{13}\) |
| B. | \(\frac{2}{11}\) |
| C. | \(\frac{3}{7}\) |
| D. | \(\frac{8}{15}\) |
| Answer» D. \(\frac{8}{15}\) | |
| 11. |
Suppose a fair eight-sided die is rolled once. If the value on the die is 1, 3, 5 or 7 the die is rolled a second time. Determine the probability that the sum of values that turn up is at least 8? |
| A. | \(\frac{32}{87}\) |
| B. | \(\frac{12}{43}\) |
| C. | \(\frac{6}{13}\) |
| D. | \(\frac{23}{64}\) |
| Answer» E. | |
| 12. |
A family has two children. Given that one of the children is a girl and that she was born on a Monday, what is the probability that both children are girls? |
| A. | \(\frac{13}{27}\) |
| B. | \(\frac{23}{54}\) |
| C. | \(\frac{12}{19}\) |
| D. | \(\frac{43}{58}\) |
| Answer» B. \(\frac{23}{54}\) | |
| 13. |
Mangoes numbered 1 through 18 are placed in a bag for delivery. Two mangoes are drawn out of the bag without replacement. Find the probability such that all the mangoes have even numbers on them? |
| A. | 43.7% |
| B. | 34% |
| C. | 6.8% |
| D. | 9.3% |
| Answer» D. 9.3% | |
| 14. |
A cupboard A has 4 red carpets and 4 blue carpets and a cupboard B has 3 red carpets and 5 blue carpets. A carpet is selected from a cupboard and the carpet is chosen from the selected cupboard such that each carpet in the cupboard is equally likely to be chosen. Cupboards A and B can be selected in \(\frac{1}{5}\) and \(\frac{3}{5}\) ways respectively. Given that a carpet selected in the above process is a blue carpet, find the probability that it came from the cupboard B. |
| A. | \(\frac{2}{5}\) |
| B. | \(\frac{15}{19}\) |
| C. | \(\frac{31}{73}\) |
| D. | \(\frac{4}{9}\) |
| Answer» C. \(\frac{31}{73}\) | |
| 15. |
A meeting has 12 employees. Given that 8 of the employees is a woman, find the probability that all the employees are women? |
| A. | \(\frac{11}{23}\) |
| B. | \(\frac{12}{35}\) |
| C. | \(\frac{2}{9}\) |
| D. | \(\frac{1}{8}\) |
| Answer» D. \(\frac{1}{8}\) | |
| 16. |
Naina receives emails that consists of 18% spam of those emails. The spam filter is 93% reliable i.e., 93% of the mails it marks as spam are actually a spam and 93% of spam mails are correctly labelled as spam. If a mail marked spam by her spam filter, determine the probability that it is really spam. |
| A. | 50% |
| B. | 84% |
| C. | 39% |
| D. | 63% |
| Answer» B. 84% | |
| 17. |
A single card is drawn from a standard deck of playing cards. What is the probability that the card is a face card provided that a queen is drawn from the deck of cards? |
| A. | \(\frac{3}{13}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{4}{13}\) |
| D. | \(\frac{1}{52}\) |
| Answer» C. \(\frac{4}{13}\) | |
| 18. |
Previous probabilities in Bayes Theorem that are changed with help of new available information are classified as _________________ |
| A. | independent probabilities |
| B. | posterior probabilities |
| C. | interior probabilities |
| D. | dependent probabilities |
| Answer» C. interior probabilities | |
| 19. |
An urn B1 contains 2 white and 3 black chips and another urn B2 contains 3 white and 4 black chips. One urn is selected at random and a chip is drawn from it. If the chip drawn is found black, find the probability that the urn chosen was B1. |
| A. | 4⁄7 |
| B. | 3⁄7 |
| C. | 20⁄41 |
| D. | 21⁄41 |
| Answer» E. | |
| 20. |
Two boxes containing candies are placed on a table. The boxes are labelled B1 and B2. Box B1 contains 7 cinnamon candies and 4 ginger candies. Box B2 contains 3 cinnamon candies and 10 pepper candies. The boxes are arranged so that the probability of selecting box B1 is 1⁄3 and the probability of selecting box B2 is 2⁄3. Suresh is blindfolded and asked to select a candy. He will win a colour TV if he selects a cinnamon candy. If he wins a colour TV, what is the probability that the marble was from the first box? |
| A. | 7⁄13 |
| B. | 13⁄7 |
| C. | 7⁄33 |
| D. | 6⁄33 |
| Answer» B. 13⁄7 | |
| 21. |
Two boxes containing candies are placed on a table. The boxes are labelled B1 and B2. Box B1 contains 7 cinnamon candies and 4 ginger candies. Box B2 contains 3 cinnamon candies and 10 pepper candies. The boxes are arranged so that the probability of selecting box B1 is 1⁄3 and the probability of selecting box B2 is 2⁄3. Suresh is blindfolded and asked to select a candy. He will win a colour TV if he selects a cinnamon candy. What is the probability that Suresh will win the TV (that is, she will select a cinnamon candy)? |
| A. | 7⁄33 |
| B. | 6⁄33 |
| C. | 13⁄33 |
| D. | 20⁄33 |
| Answer» D. 20⁄33 | |
| 22. |
A box of cartridges contains 30 cartridges, of which 6 are defective. If 3 of the cartridges are removed from the box in succession without replacement, what is the probability that all the 3 cartridges are defective? |
| A. | \(\frac{(6*5*4)}{(30*30*30)}\) |
| B. | \(\frac{(6*5*4)}{(30*29*28)}\) |
| C. | \(\frac{(6*5*3)}{(30*29*28)}\) |
| D. | \(\frac{(6*6*6)}{(30*30*30)}\) |
| Answer» C. \(\frac{(6*5*3)}{(30*29*28)}\) | |
| 23. |
Previous probabilities in Bayes Theorem that are changed with help of new available information are classified a? |
| A. | independent probabilities |
| B. | posterior probabilities |
| C. | interior probabilities |
| D. | dependent probabilities |
| Answer» C. interior probabilities | |
| 24. |
At a certain university, 4% of men are over 6 feet tall and 1% of women are over 6 feet tall. The total student population is divided in the ratio 3:2 in favour of women. If a student is selected at random from among all those over six feet tall, what is the probability that the student is a woman? |
| A. | <sup>2</sup>‚ÅÑ<sub>5</sub> |
| B. | <sup>3</sup>‚ÅÑ<sub>5</sub> |
| C. | <sup>3</sup>‚ÅÑ<sub>11</sub> |
| D. | <sup>1</sup>‚ÅÑ<sub>100</sub> |
| Answer» D. <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>100</sub> | |
| 25. |
An urn B1 contains 2 white and 3 black chips and another urn B2 contains 3 white and 4 black chips. One urn is selected at random and a chip is drawn from it. If the chip drawn is found black, find the probability that the urn chosen was B1. |
| A. | <sup>4</sup>‚ÅÑ<sub>7</sub> |
| B. | <sup>3</sup>‚ÅÑ<sub>7</sub> |
| C. | <sup>20</sup>‚ÅÑ<sub>41</sub> |
| D. | <sup>21</sup>‚ÅÑ<sub>41</sub> |
| Answer» E. | |
| 26. |
Suppose box A contains 4 red and 5 blue coins and box B contains 6 red and 3 blue coins. A coin is chosen at random from the box A and placed in box B. Finally, a coin is chosen at random from among those now in box B. What is the probability a blue coin was transferred from box A to box B given that the coin chosen from box B is red? |
| A. | <sup>15</sup>‚ÅÑ<sub>29</sub> |
| B. | <sup>14</sup>‚ÅÑ<sub>29</sub> |
| C. | <sup>1</sup>‚ÅÑ<sub>2</sub> |
| D. | <sup>7</sup>‚ÅÑ<sub>10</sub> |
| Answer» B. <sup>14</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>29</sub> | |
| 27. |
Two boxes containing candies are placed on a table. The boxes are labelled B1 and B2. Box B1 contains 7 cinnamon candies and 4 ginger candies. Box B2 contains 3 cinnamon candies and 10 pepper candies. The boxes are arranged so that the probability of selecting box B1 is 1‚ÅÑ3 and the probability of selecting box B2 is 2‚ÅÑ3. Suresh is blindfolded and asked to select a candy. He will win a colour TV if he selects a cinnamon candy. If he wins a colour TV, what is the probability that the marble was from the first box?$ |
| A. | <sup>7</sup>‚ÅÑ<sub>13</sub> |
| B. | <sup>13</sup>‚ÅÑ<sub>7</sub> |
| C. | <sup>7</sup>‚ÅÑ<sub>33</sub> |
| D. | <sup>6</sup>‚ÅÑ<sub>33</sub> |
| Answer» B. <sup>13</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>7</sub> | |
| 28. |
Two boxes containing candies are placed on a table. The boxes are labelled B1 and B2. Box B1 contains 7 cinnamon candies and 4 ginger candies. Box B2 contains 3 cinnamon candies and 10 pepper candies. The boxes are arranged so that the probability of selecting box B1 is 1‚ÅÑ3 and the probability of selecting box B2 is 2‚ÅÑ3. Suresh is blindfolded and asked to select a candy. He will win a colour TV if he selects a cinnamon candy. What is the probability that Suresh will win the TV (that is, she will select a cinnamon candy)?$ |
| A. | <sup>7</sup>‚ÅÑ<sub>33</sub> |
| B. | <sup>6</sup>‚ÅÑ<sub>33</sub> |
| C. | <sup>13</sup>‚ÅÑ<sub>33</sub> |
| D. | <sup>20</sup>‚ÅÑ<sub>33</sub> |
| Answer» D. <sup>20</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>33</sub> | |
| 29. |
Three companies A, B and C supply 25%, 35% and 40% of the notebooks to a school. Past experience shows that 5%, 4% and 2% of the notebooks produced by these companies are defective. If a notebook was found to be defective, what is the probability that the notebook was supplied by A? |
| A. | <sup>44</sup>‚ÅÑ<sub>69</sub> |
| B. | <sup>25</sup>‚ÅÑ<sub>69</sub> |
| C. | <sup>13</sup>‚ÅÑ<sub>24</sub> |
| D. | <sup>11</sup>‚ÅÑ<sub>24</sub> |
| Answer» C. <sup>13</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>24</sub> | |