Question

A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II, III are p, q and 1/2, respectively. If the probability that the student is successful is 1/2, then possible value of p and q are -

• A. p = q = 1
• B. p = q = ½
• C. p = 1, q = 0
• D. p = 1, q = ½

Answer 1

Answer: (C)

p = 1, q = 0

Answer 2

Let A, B and C be the events that the student is

successful in tests I, II and III, respectively.

Then P (the student is successful)

= P [(A Ē B Ē C¢) Č (A Ē B¢ Ē C) Č (A Ē B Ē

= P (A Ē B Ē C¢) + P (A Ē B¢ Ē C) + P (A Ē B Ē C)

= P (1) P (2) P (C¢) + P (1) P (B¢) P (3) + P (1) P (2) P (C

[Q A, B and C are independent]

= pq (1 – 1/2) + p (1 – q) (1/2) + (pq) (1/2)

= $\frac { 1 } { 2 }$[pq + p (1 – q) + pq] = $\frac { 1 } { 2 }$p(1 + q)

\ $\frac { 1 } { 2 }$ = $\frac { 1 } { 2 }$ p (1 + q) Ž p (1 + q) = 1

This equation is satisfied for pair of values in (3)