Question

A student appears for test 1,2 and 3. The student is successul if he passes either in tests 1 and 2 or tests 1 and 3. The probability of student passing in tests 1,2 and 3 is a,b,$\frac{1}{2}$ respectively.If the probability that the student is successful is $\frac{1}{2}$. Then,

• A. a=b=1
• B. a=b=1/2
• C. a=1 and b=0
• D. a=1 and b=1/2

Answer 1

The correct option is C

a=1 and b=0

$P\left(PFP\right)+P\left(PPP\right)+P\left(PPF\right)=\frac{1}{2}$

$a\times (1-b)\times \frac{1}{2}+\frac{ab}{2}+\frac{ab}{2}=\frac{1}{2}$

$a(1-b)+2ab=1$

$a+ab=1$

This is possible only when $a=1$ and $b=0$