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A JEE aspirant estimates that she will b...

A JEE aspirant estimates that she will be successful with an 80 percent chance if she studies 10 hours per day, with a 60 percent chance if she studies 7 hours per day and with 40 percent chance if she studies 4 hours per day. She further believes that she will study 10 hours, 7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7 respectively. Given that she will achieve success, the chance she studied for 4 hours is?

A

`(14)/(19)`

B

`(1)/(4)`

C

`(7)/(12)`

D

`(2)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
`p(10hr)=.1" "p(s//10hr)=.8`
`p(7hr)=.2" "p(s//7hr)=.6`
`p(4hr)=.7" "p(s//4hr)=.4`
`p(s)=.1xx.8+.2xx.6+.7xx.4`
`p(4hr//s)=(.7xx.4)/(.1xx.8+.2xx.6+.7xx.4)=(28)/(8+12+28)=(28)/(48)=(7)/(12)`
`|(1,-lamda,-1),(lamda,-1,-1),(1,1,-1)|ne0`
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A JEE aspirant estimates that she will be successful with an 80 percent chance if she studies 10 hours per day, with a 60 percent chance if she studies 7 hours per day and with 40 percent chance if she studies 4 hours per day. She further believes that she will study 10 hours, 7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7 respectively. Given that she does not achieve success, the chance she studied for 4 hours is?

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