Question

Find the probability that a number selected at random from the numbers 1, 2, 3, ..., 34 , 35 is (a) a prime number, (b) a multiple of 7, (c) a multiple of 3 or 5.

Answer 1

The possible outcomes are 1, 2, 3, 4, 5................35.
Number of all possible outcomes = 35

(a) Out of the given numbers, the prime numbers are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

Let E₁ be the event of getting a prime number.
Then,​ number of favourable outcomes =​ 11
∴ P (getting a prime number) = P(E₁ ) = $\frac{11}{35}$

(b) Out of the given numbers, the numbers that are multiples of 7 are

7, 14, 21, 28 and 35.

Let E₂ be the event of getting a multiple of 7.

Then,​ number of favourable outcomes = 5
∴ P (getting a multiple of 7 ) = P(E₂ ) $\frac{5}{35}=\frac{1}{7}$

(c) Out of the given numbers, the numbers that are multiples of 3 are

3, 6, 9, 12, 15, 18, 21, 24, 27, 30 and 33.
And the multiples of 5 are 5, 10, 15, 20, 25, 30 and 35.

Let E₃ be the event of getting a multiple of 3 or 5.

Then,​ number of favourable outcomes = (11 + 7 − 2) = 16

∴ P (getting a multiple of 3 or 5 ) = P(E₃ ) = $\frac{16}{35}$