In an entrance test that is graded on the basis of two examinations the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both ?
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Step - 1 : Assume two events and consider the condition.
Suppose that , A is event of passing the first exam.
and B is the event of passing second exam.
Given that probability of randomly chosen student passing first exam is
0.8 and passing second exam is 0.7.
so , p(A) = 0.8
p(B) = 0.7
Also given that probability of passing at least one of the exam is 0.95.
so p⊂A∪B = 0.95
Step - 2 : Find probability of passing both exam.
So event of passing both is (A∩B)
So we have to find P(A∩B)
As per rule we know P(A∪B) = P(A) + P(B) − P(A∩B)
⇒ P(A∩B) = P(A) + P(B) − P(A∪B)
⇒ P(A∩B) = 0.8 + 0.7 − 0.95
⇒ P(A∩B) = 0.55
Hence, Probability of passing both exam is 0.55
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