Question

A box contains 36 cards, bearing only one number from 1 to 36 on each. If one card is drawn at random, find the probability of an event that the card drawn bears, a prime number

Answer 1

Sample space,

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12, 13, 14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28, 29, 30,

31, 32, 33, 34, 35, 36}

∴ n(S) = 36

Let B be the event that the card drawn bears a prime number.

∴ B = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}

∴ n(B) = 11

∴ P(B) = `("n"("B"))/("n"("S"))`

∴ P(B) = `11/36`