Question

In a single throw of two dice, find the probability of obtaining 

(i) sum of less than 5 

(ii) a sum of greater than 10 

(iii) a sum of 9 or 11.

Answer 1

The sample space when throwing two dice once 

= {(1, 1), (1, 2), … (1, 6) 

(2, 1), … (2, 6) 

: 

:

(6, 1), … (6, 6)} 

n(S) = 6² = 36 

(i) Let A be the event of getting a sum less than 5. 

Then A = {(1, 1), (1, 2), (1, 3) (2, 1),(2, 2) (3, 1)} 

n(A) = 6 

∴ P(A) = n(A)/n(S) = 6/36 = 1/6

(ii) Let B be the event of getting a sum greater than 10. 

∴ The sum will be 11 or 12. 

Now the numbers whose sum is 11. 

= {(5, 6), (6, 5)} 

The number whose sum is 12 = {(6, 6)} 

n(B) = 2 + 1 = 3 

∴ P(B) = 3/36 = 1/12

(iii) Let C be the event of getting a sum 9 or 11. 

Now C = {(3, 6), (4, 5) (5, 4), (6, 3) (5, 6), (6, 5)} 

n(C) = 6 

∴ P(C) = 6/36 = 1/6