State whether the statement are True or False.If A and B are two cand

1.	State whether the statement 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?
Answer» 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.

State whether the statement 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?

Answer»

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.

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State whether the statement 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?

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