Q. 214.3( 4 Votes )

# In an entrance te

Answer :

Let E denotes the event that student passed in first examination.

And H be the event that student passed in second exam.

Given, P(E) = 0.8 and P(H) = 0.7

Also probability of passing atleast one exam i.e P(E or H) = 0.95

Or, P(E H) = 0.95

We have to find the probability of the event in which students pass both the examinations i.e. P(E H)

Note: By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that:

P(A B) = P(A) + P(B) – P(A B)

P(E H) = P(E) + P(H) – P(E H)

P(E H) = P(E) + P(H) – P(E H)

P(E H) = 0.7 + 0.8 – 0.95 = 1.5 – 0.95 = 0.55

Probability of passing both the exams = P(E H) = 0.55

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