are two candidates seeking admission in I.I.T. The probability that P is selected is 0.5 and the probability that both  are selected is at most 0.3. Prove that the probability of  being selected is at most 0.8

Explanation

To solve the problem, we need to establish the relationship between the probabilities of the two candidates being selected for admission to IIT. Let's denote:

- \( P(A) \): Probability that candidate P is selected = 0.5
- \( P(B) \): Probability that candidate Q is selected (which we need to find)
- \( P(A \cap B) \): Probability that both candidates are selected = at most 0.3

We need to prove that \( P(B) \) is at most 0.8.

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