A final year student appears for placement interview in two companies, S and…
2025
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. 0.4 ≤ 𝑝 ≤ 0.6 — Let \(S\) and \(T\) denote the events of receiving offers from the two companies. Then \(P(S)=0.8\), \(P(T)=0.6\), and \(p=P(S\cap T)\). Since \(P(S\cup…
- A.
0 ≤ 𝑝 ≤ 0.2
- B.
0.4 ≤ 𝑝 ≤ 0.6
- C.
0.2 ≤ 𝑝 ≤ 0.4
- D.
0.6 ≤ 𝑝 ≤ 1.0
Show answer & explanation
Correct answer: B
Let \(S\) and \(T\) denote the events of receiving offers from the two companies. Then \(P(S)=0.8\), \(P(T)=0.6\), and \(p=P(S\cap T)\). Since \(P(S\cup T)=P(S)+P(T)-p\le 1\), we get \(p\ge0.8+0.6-1=0.4\). Also \(S\cap T\subseteq T\), so \(p\le P(T)=0.6\). Hence \(0.4\le p\le0.6\).