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The probability that a student will pass in French is 0.64, will pass in Sociology is 0.45, and will pass in both is 0.40. What is the probability that the student will pass in at least one - Mathematics and Statistics

Sum

The probability that a student will pass in French is 0.64, will pass in Sociology is 0.45, and will pass in both is 0.40. What is the probability that the student will pass in at least one of the two subjects?

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Solution

Let event A: The student will pass in French.

∴ P(A) = 0.64

Let event B: The student will pass in Sociology.

 ∴ P(B) = 0.45

Also, P(A ∩ B) = 0.40

∴  Required probability

= P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= 0.64 + 0.45 – 0.40

= 0.69

Concept: Addition Theorem for Two Events
  Is there an error in this question or solution?
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