If odds against solving a question by three students are 2:1, 5:2, and 5:3, respectively, then probability that the question is solved only by one student is a.`31//56` b. `24//56` c. `25//56` d. none of these

Options

A. `31//56`
B. `24//56`
C. `23//56`
D. None of these

Answer

C

Explanation

The probabilities of solving the question by these three students are `1//3,2//7and 3//8,` respectively. Therefore,
`P(A)=(1)/(3),P(B)=2/7,P(C)=3/8`
Then probability of question solved by only one student is `P((A barBbarCor barABbarCorbarAbarBC))`
`=P(A)P(barB)P(barC)+P(barA)P(B)P(barC)+P(barA)P(barB)P(C)`
`=P(A)P(barB)P(barC)+P(barA)P(B)P(barC)+P(barA)P(barB)P(C)`
`=1/3xx5/7xx5/8xx2/3xx2/7xx5/8+2/3xx5/7xx3/8`
`=(25+20+30)/(168)=25/56`