In a game, a number is chosen at random from the set 1,2,3, . . .

Question : In a game, a number is chosen at random from the set 1,2,3, . . .28,29,30. The probability that the number chosen is a product of exactly two different prime numbers is 

a) 5/30

b) 2/30

c) 7/30

d) none of these.

Doubt by Zoha

Solution : 

Total Number of possible outcomes 

{1,2,3. . .30} = 30

Numbers which are product of exactly two different prime numbers 
{6,10,14, 15, 21, 22, 26} = 7

P(Event) =
No. of favorable outcomes / Total No. of possible outcomes

P(Number is a product of exactly two different prime numbers) = 7/30

Hence, c) would be the correct option.