Question

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.

• A. \( 0 \leq p \leq 0.2 \)
• B. \( 0.4 \leq p \leq 0.6 \)
• C. \( 0.2 \leq p \leq 0.4 \)
• D. \( 0.6 \leq p \leq 1.0 \)

Hint:

When calculating the probability of two independent events occurring together, multiply their individual probabilities.

Answer 1

The Correct Option is B

Let the probability of receiving a job offer from company \( S \) be \( P(S) = 0.8 \) and the probability of receiving a job offer from company \( T \) be \( P(T) = 0.6 \). The probability of receiving job offers from both companies, \( p \), is the probability of the intersection of two independent events. For independent events, the probability of both events happening is the product of the individual probabilities: \[ p = P(S \cap T) = P(S) \times P(T) = 0.8 \times 0.6 = 0.48 \] Therefore, the probability that the student receives job offers from both companies is \( p = 0.48 \). Now, let's analyze the options:
Option (A): \( 0 \leq p \leq 0.2 \) does not contain \( p = 0.48 \).
Option (B): \( 0.4 \leq p \leq 0.6 \) contains \( p = 0.48 \).
Option (C): \( 0.2 \leq p \leq 0.4 \) does not contain \( p = 0.48 \).
Option (D): \( 0.6 \leq p \leq 1.0 \) does not contain \( p = 0.48 \).
Thus, the correct answer is option (B) \( 0.4 \leq p \leq 0.6 \).