Concept of “Probability”-02

Question: When two dice are thrown, what is the probability that the sum of the numbers appeared is  8 ? [Ans. (b) 13/18] 

(a) 17/18   (b) 13/18   (c) 13/28  (d) 15/18  (e) None of these

Solution:

Detailed Explanation:

Concept: Probability is the ratio of n(E) to n(S); that is the no. of favorable cases to the total no. of outcomes.

When two dice are thrown, then the sample space is given by

S = S₁×S₂ , where S_{1 =} {1,2,3,4,5,6} and   S₂ = {1,2,3,4,5,6}

Or, S = {1,2,3,4,5,6}×{1,2,3,4,5,6} = {(1,1), (1,2), (1,3), ……….(6,6)} = 36

Or, n(S) = 36

It can also be determined as

n(S) = n(S₁)×n(S₂) = 6 × 6 = 36

Sum of the digits		n(E)
2	12	1
3	11	2
4	10	3
5	9	4
6	8	5
7		6

n(E) = Sum is either 8 or 7 or 6 or 5 or 4 or 3 or 2 = 5+6+5+4+3+2+1 = 26

Probability = n(E)/n(S) = 26/36 = 13/18 Ans.

=======================================================================