ProbabilityHard
Question
A student appears for tests I, II & III. The student is successful if he passes either in tests I & II or tests I & III. The probabilities of the student passing in the tests I, II & III are p, q & 1/2 respectively. If the probability that the student is successful is 1/2, then:
Options
A.p = 1, q = 0
B.p = 2/3, q = 1/2
C.p = 3/5, q = 2/3
D.there are infinitely many values of p & q.
Solution
P(T 1) = p
P(T 2) = q
P(T 3) = 1/2
= P(T 1, T 2) + P(T 1, T3) + P(T 1 T 2 T 3)
= pq 1/2 + p(1 - q) 
+ pq 
= 
+ p ⇒ 1 = pq + 2p.
Now, check options.
P(T 2) = q
P(T 3) = 1/2
= P(T 1, T 2) + P(T 1, T3) + P(T 1 T 2 T 3) = pq 1/2 + p(1 - q) + pq = + p ⇒ 1 = pq + 2p.Now, check options.
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