Two students X and Y appeared in an examination. The probability that X will qualify the examination is 0.05 and Y will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. What is the probability that only one of them will qualify the examination?

Two students X and Y appeared in an examination. The probability that X will qualify the examination is 0.05 and Y will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. What is the probability that only one of them will qualify the examination? Correct Answer 0.11

Concept:

Formulas used:

• P(A) = 1 – P(A̅)
• P(A̅ ∩ B) = P(A) – P(A ∩ B)

Calculation:

Let,

X: Event that X will qualify the examination.

Y: Event that Y will qualify the examination.

Given: P(X) = 0.05, P(Y) = 0.10, P(X ∩ Y) = 0.02

P (only one of them will qualify) = P(X and not Y) + P(Y and not X)

= P(X ∩ Y̅) + P(X̅ ∩ Y)

= P(X) – P(X ∩ Y) + P(Y) – P(X ∩ Y)

= P(X) + P(Y) – 2P(X ∩ Y)

= 0.05 + 0.10 – 2(0.02)

= 0.15 – 0.04

= 0.11