Question

Two candidates A and B attended an interview for two jobs. The probability that A gets the job is 0.8, and for B it is 0.7. What is the probability that at least one of them gets a job?

• A. 0.96
• B. 0.94
• C. 0.92
• D. 0.9

Hint:

Use the identity: \( P(A \cup B) = 1 - P(\bar{A} \cap \bar{B}) \) for calculating “at least one” type probabilities.

Answer 1

The Correct Option is B

Let \( P(A) = 0.8,\ P(B) = 0.7 \). Then, the probability that neither gets the job is: \[ P(\bar{A} \cap \bar{B}) = (1 - 0.8)(1 - 0.7) = 0.2 \times 0.3 = 0.06 \] Hence, probability that at least one gets the job is: \[ P(A \cup B) = 1 - P(\bar{A} \cap \bar{B}) = 1 - 0.06 = 0.94 \]