Q33 of 43 Page 296

State whether the statements are True or False

If A and B are two candidates seeking admission in an engineering College. The probability that A is selected is .5 and the probability that both A and B are selected is at most .3. Is it possible that the probability of B getting selected is 0.7?

Let E1 be the event that A is selected in engineering college

and E2 be the event that B is selected in engineering college


Then, we have


P(E1) = 0.5, P(E2) = 0.7 and P(E1⋂ E2) ≤ 0.3


Now, P(E1) × P(E2) ≤ 0.3


⇒ 0.5 × P(E2) ≤ 0.3


⇒ P(E2) ≤ 0.6


But P(E2) = 0.7


Hence, the given statement is False.


More from this chapter

All 43 →
31

State whether the statements are True or False

The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.

 32

State whether the statements are True or False

The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11.

 34

State whether the statements are True or False

The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.

 35

State whether the statements are True or False

The probability of an occurrence of event A is .7 and that of the occurrence of event B is .3 and the probability of occurrence of both is .4.