Question

The 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 will not succeed at both the places is

Answer 1

Answer:

P(not succeeing both the places) is 0.6

Step-by-step explanation:

Formula used:

Let A and B be two events.

Then

P(AUB) = P(A)+P(B) - P(A∩B)

Let A be the event of succeeding in IIT entrance test and B be the event of succeeding in Roorkee entrance test.

Given:

P(A)=0.2

P(B)=0.5

P(A∩B)=0.3

⇒

P(AUB) = P(A)+P(B) - P(A∩B)

P(AUB) = 0.2+0.5 - 0.3

P(AUB) = 0.7 - 0.3

P(AUB) = 0.4

Now,

P(not succeeding both the places)

$=P(\bar{A}$∩$\bar{B})$

$=P(\bar{A}\bar{U}\bar{B})$

$=1-P(AUB)$

$=1-0.4$

$=0.6$