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Question

Given that she does not achieve success, the chance she studied for 4 hour, is

A
1826
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B
1926
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C
2026
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D
2126
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Solution

The correct option is D 2126
Given,The probability of a Jee Aspirant to be successful if he studies for 10 hours per day,P(t10)=0.8
The probability of a Jee Aspirant to be successful if he studies for 7 hours per day,P(t7)=0.6
The probability of a Jee Aspirant to be successful if he studies for 4 hours per day,P(t4)=0.4
The probability that she will study 10 hours per day,P(A)=0.1
The probability that she will study 7 hours per day,P(B)=0.2
The probability that she will study 4 hours per day,P(C)=0.7
Theprobabilitythatshewillbesuccessful,P(S)=P(t10)P(A)+P(t7)P(B)+P(t4)P(S/t4)
=0.80.1+0.60.2+0.40.7=0.48
The probability that she will not success,P(¯¯¯¯S)=1P(S)=10.48=0.52
But probability that she studies 4 hours per day but didn't success=P(¯t4C)=P(¯t4)P(C)=(10.4)0.7=0.42
Since (A,t10),(B,t7),(C,t4) pairwise independent P(AB)=P(A).P(B)
If (A,t10),(B,t7),(C,t4) are independent,then (A,¯t10),(B,¯t7),(C,¯t4),(¯¯¯¯A,t10),(¯¯¯¯B,t7),(¯¯¯¯C,t4) will also be independent.
The probability that she studies 4 hours per day given she is not successful,P(C/¯¯¯¯S)=P(C¯¯¯¯S)P(¯¯¯¯S)
=0.420.52=2126

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