The odds against solving a problem by A and B are 3 :2 and 2 : 1 respectively, then the probability that the problem will be solved, is

Options

A. ` ( 3 ) /( 5 ) `
B. ` ( 2 ) /( 15 ) `
C. ` ( 2 ) /( 5 ) `
D. ` ( 11 ) /( 5 ) `

Answer

A

Explanation

Given ` P ( A) = ( 3 ) /( 2 + 3 ) = ( 3 ) / ( 5 ) , P (B) = ( 2 )/ ( 2 + 1 ) = (2 ) / (3 ) `
and ` P ( barA ) = 1 - ( 3 ) /( 5 ) = ( 2 ) /( 5 ) , P ( bar B ) = 1 - ( 2 )/ (3 ) = (1 ) / ( 3 ) `
` therefore ` Required probability
` = P ( A nn bar B ) + P ( barA nn B ) + P ( bar A nn bar B ) `
` = P (A) * P (barB) + P ( barA ) * P (B) + P (bar A ) * P (barB) `
` = ( 3 )/( 5 ) * ( 1) /( 3 ) + ( 2 ) /( 5 ) * ( 2 ) /(3 ) + ( 2 )/( 5 ) * (1)/( 3 ) `
` = ( 1 )/( 5 ) + ( 4 ) /( 15 ) + ( 2 )/( 15 ) `
`= ( 3 + 4 + 2 ) /( 15 ) = ( 9 ) /( 15 ) = ( 3 )/( 5 ) `