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Question

The probability that a student will succeed in the IIT entrance test is 0.2 and that he will succeed in the Roorkee entrance test is 0.5. If the probability that he will be successful at both the places is 0.3, then the probability that he does not succeed at both places is


A

0.4

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B

0.3

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C

0.2

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D

0.6

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Solution

The correct option is D

0.6


Explanation for the correct answer:

Finding the value of P(A'B'):

Let, A be the event that a student succeeds in the IIT entrance test and B be the event that a student succeeds in the Roorkee entrance test.

Given that, P(A)=0.2,P(B)=0.5,P(AB)=0.3

Thus, the probability that a student does not succeed in both places =P(A'B')

P(A'B')=1-P(AUB)[Formulaofintersection]P(A'B')=1-[P(A)+P(B)-P(AB)][Formulaofunion]

Now, substituting the values

P(A'B')=1-[0.2+0.5-0.3]P(A'B')=1-0.4P(A'B')=0.6

Therefore, the correct answer is option (D).


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