Question

A student appears for tests I, II and III. The student is successful if he passes either in test I and II or test I and test III. The probability of the student passing the tests I, II and III are p, q, and ½ respectively. If the probability that the student is successful is ½, then

• A. p=q=1
• B. p=q=1/2
• C. p=1, q=0
• D. p=1, q=1/2

Answer 1

Answer: (C)

p=1, q=0

Answer 2

Let A, B, C denote the events of passing the tests I, II and III respectively; clearly they are independent event.

According to question,

$\frac { 1 } { 2 } = \mathrm { P } [ ( \mathrm { A } \cap \mathrm { B } ) \mathrm { U } ( \mathrm { A } \cap \mathrm { C } ) ]$

= P(

= P(1) P(2) + P(1) P(3) – P(1) P(2) P(3)

$\frac { 1 } { 2 } = p q + \frac { p } { 2 } - \frac { p q } { 2 }$

Or, 1 = 2 pq + q – pq = p (q+1)