Find the probability that a number selected at random from the numbers 1, 2,3,……… 34, 35 is

a) a prime number b ) is a multiple

Given set of numbers are: 1, 2, 3, 4, ........, 34, 35.

**a)**

Let A be the event of selecting a prime number out of given set of numbers.

Favourable outcomes to event A = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31

Therefore, number of favourable outcomes = 11

Total number of outcomes = 35

**b)**

Let B be the event of selecting a multiple of 7.

Favourable outcomes to event B = 7, 14, 21, 28 and 35

Therefore, number of favourable outcomes = 5

Total number of outcomes = 35

**c)**

Let *C* be the event of selecting a number which is multiple of 2 and 5.

Favourable outcomes to event C = 10, 20 and 30

Therefore, number of favourable outcomes = 3

Total number of outcomes = 35

**d)**

Let D be the event of selecting a number which is multiple of 2 or 3.

Favourable outcomes to event D = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 3, 9, 15, 21, 27 and 33.

Therefore, number of favourable outcomes = 23

Total number of outcomes = 35

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