A JEE aspirant estimates that she will be successful with an `80%` chance if she studies 10 hours per day, with `60%` chance if she studies 7 hourse per day, and with a `40%` chance if she studies 4 hours per day. She further believes that she will study 10 houers, 7 hours, and 4 hours per day with probabilities `0.1,0.2and 0.7,` respectively.
The chance she will be successful is

Options

A. `0.28`
B. `0.38`
C. `0.48`
D. `0.58`

Answer

C

Explanation

A: She gets a success
T: She studies 10 h, P(T) = 0.1
S: She studies 7 h: `P(S)=0.2`
F: She studies `4 h: P(F) =0.7`
`P(A//T)=0.8,P(A//S)=0.6,P(A//F)=0.4`
`P(A)-P(AnnT)+P(AnnS)+P(AnnF)`
`=(0.1)(0.8)+(0.2)(0.6)+(0.7)(0.4)`
`=0.08+0.12+0.28=0.48`
`=P(F//A)=(P(FnnA))/(P(A))`
`=((0.7)(0.4))/(0.48)`
`(0.28)/(0.48)=7/12`
`=P(F//A)=(P(FnnA))/(P(A))`
`=((0.7)(0.4))/(0.48)`
`P(F//barA)=(P(FnnbarA))/(P(barA))`
`=(P(F)-P(FnnA))/(0.52)`
`=((0.7)-0.28)/(0.52)`
`=(0.42)/(0.52)=21/26`