Discussion
A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from companies S and T to be 0.8 and 0.6, respectively. Let \(p\) be the probability that she receives job offers from both the companies. Select the most appropriate option.
Answer: B
The most appropriate range is \(0.4 \le p \le 0.6\).
For any two events, \(P(S \cap T) \ge P(S) + P(T) - 1 = 0.8 + 0.6 - 1 = 0.4\), because the union cannot have probability above 1. And \(P(S \cap T) \le \min(0.8, 0.6) = 0.6\), since the intersection cannot exceed either event.
If the offers are independent, \(p = 0.48\), inside this range. Values below 0.4 are impossible, which rules out the first and third options, and values above 0.6 are impossible, ruling out the last.
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