**Question:**

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

(i) prime number

(ii) multiple of 7

(iii) a multiple of 3 or 5

**Solution:**

GIVEN: A number is selected from numbers 1 to 35

TO FIND: Probability of getting a number

(i) which is a prime number

(ii) multiple of 7

(iii) multiple of 3 or 5

Total number of cards is 35

(i) Numbers that are primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31

Total prime numbers from 1 to 35 are11

We know that PROBABILITY =

Hence probability of getting a number which is a prime from 1 to 35 is equal to

(ii) Numbers that are multiple of 7 are 7,14,21,28,35

Total number that are multiple of 7 from 1 to 35 are5

We know that PROBABILITY =

Hence probability of getting number that is multiple of 7 from 1 to 35 is

(iii) Numbers that are multiple of 3 and 5 are 3, 5, 6, 8, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30, 33 and 35

Total numbers that are multiple of 3 or 5 from 1 to 35 is 16

We know that PROBABILITY =

Hence probability of getting number that is multiple of 3 or 5 from 1 to 35 is equal to