Question

two dices are thrown find the probability that the number obtained (I) have a sum less than 7( II) have a product less than 16 (III) is a doublet of odd number

Answer 1

For the sample space, refer the attachment.

So, Number if elements in the sample space ===> n(S) = 36


1)Let A be the event of getting a sum less than 7.

A = {(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(4,1),(4,2),(5,1)}

No. of elements of A, n(A) = 15

Probability of A, P(A) = n(A)/n(S) ====> 15/36

2) Let B be the event of getting a product less than 16.

B = {(1,1),(1,2),(1,3),(,1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(6,1),(6,2)}

No. of elements of B,n(B) = 25

Probability of B, P(B) = n(B) / n(S) ==> 25/36

3) Let C be the event of getting a doublet of odd number.

C = {(1,1),(3,3),(5,5)}

No. of elements of C, n(C) = 5

Probability of C, P(C) = n(C) / n(S) ==> 5/36