Question

A student appears for test 1, 2 and 3. The student is successful 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(PFP)+P(PPP)+P(PPF)= $\frac{1}{2}$

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

a(1-b)+2ab=1

a+ab=1

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