Question

Probability that a student will succeed in IIT entrance test is 0.2 and that he will succeed in 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 the places is

• A. 0.4
• B. 0.3
• C. 0.2
• D. 0.6

Answer 1

The correct option is D 0.6

Let A denotes the event that the student is selected in IIT entrance test and B denotes the event that he is selected in Roorkee entrance test. Then
$P\left(A\right)=0.2,P\left(B\right)=0.5$ and $P(A\cap B)=0.3$
Required probability = $P(\overline{A}\cap \overline{B})-1-P(A\cup B)$
$=1-\left(P\right(A)+P(B)-P(A\cap B\left)\right)=1-(0.2+0.5-0.3)=\mathrm{0.6.}$