-->

Probability

Question
CBSEENMA12033713

Balwant and Kulwant appeared for an interview. The probability of their selection is 1 third space and space 1 fifth respectively. Find the probability only of them selected.

Solution

Let A : Balwant is selected
B : Kulwant is selected
therefore space space space straight P left parenthesis straight A right parenthesis space equals space 1 third comma space space straight P left parenthesis straight B right parenthesis space equals 1 fifth
P(only one is selected) = P('A and not B' or B' and not A')
                           = P (A and not B) + P(B and not A)
                           = P(A) P(not B) + P(B) P(not A)
                           = P(A) [1 - P(B)] + P(B) [1 - P(A)]
                          = 1 third open parentheses 1 minus 1 fifth close parentheses space plus space 1 fifth space open parentheses 1 minus 1 third close parentheses
                          equals space 1 third cross times 4 over 5 plus 1 fifth cross times 2 over 3 space equals 4 over 15 plus 2 over 15 equals 6 over 15 equals space 2 over 5

Some More Questions From Probability Chapter