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Tickets numbered 2, 3, 4, 5, …, 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is
(i) an even number
(ii) a number less than 16
(iii) a number which is a perfect square
(iv) a prime number less than 40
Tickets numbered 2, 3, 4, 5, …, 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is
(i) an even number
(ii) a number less than 16
(iii) a number which is a perfect square
(iv) a prime number less than 40
Tickets numbered 2, 3, 4, 5,….., 100, 101 are placed in a box and mix thoroughly one ticket is drawn at random from the box. Find the probability that the number on the ticket is
(i) An even number
(ii) A number less than 16
(iii) A number which is a perfect square
(iv) A prime number less than 40.
Tickets numbered 2, 3, 4, 5,….., 100, 101 are placed in a box and mix thoroughly one ticket is drawn at random from the box. Find the probability that the number on the ticket is
(i) An even number
(ii) A number less than 16
(iii) A number which is a perfect square
(iv) A prime number less than 40.
All possible outcomes are 2, 3, 4, 5,……, 101
Number of all possible outcomes = 100
(i) Out of these the numbers that are even = 2, 4, 6, 8,……,100
Let E1 be the event of getting an even number.
Then, number of favorable outcomes = 50
Tn = 100
⇒ 2 + (n – 1) x 2 = 100,
⇒ n = 50
therefore, P(getting an even number) = \(\frac{50}{100}\) = \(\frac{1}{2}\)
(ii) Out of these, number that are less than 16 = 2, 3, 4, 5,…….,15.
Let E2 be the event of getting a number less than 16.
Then, number of favorable outcomes = 14
therefore, P(getting a number less than 16) = \(\frac{14}{100}\) = \(\frac{7}{50}\)
(iii) Out of these, number that are perfect square = 4, 9, 16, 25, 36, 49, 64, 81 and 100
Let E3 be the event of getting a number that is a perfect square.
Then, number of favorable outcomes = 9
therefore, P(getting a number that is a perfect square) = \(\frac{9}{100}\)
(iv) Out of these, prime number less than 40 = 2,3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.
Let E4 be the event of getting a prime number less than 40.
Then, number of favorable outcomes = 12
Therefore, P(getting a prime number less than 40) = \(\frac{12}{100}\) = \(\frac{3}{25}\)
Tickets numbered 2, 3, 4, 5, …, 100, 101
Total number of tickets = 100
(i) Even numbers from 2 to 101 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100
Total number of even number = 50
P(getting a even number) = 50/100 = 1/2.
(ii) Numbers less than 16 from 2 to 101 = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Total number of numbers less than 16 = 14
P(getting a number less than 16) = 14/100 = 7/50.
(iii) Perfect square from 2 to 101 = 4, 9, 16, 25, 36, 49, 64, 81, 100
Total number of perfect squares = 9
P(getting a perfect square) = 9/100.
(iv) Prime numbers less than 40 from 2 to 101 = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
Total number of prime numbers = 12
P(getting a prime number less 40) = 12/100 = 3/25.