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There are 2 candidates A and B. Probability that A will crack the exam is 3/4 and that B will crack the exam is 2/3. What will be the probability that only one will crack the exam?

There are 2 candidates A and B. Probability that A will crack the exam is 3/4 and that B will crack the exam is 2/3. What will be the probability that only one will crack the exam? Correct Answer 5/12

Given:

Probability that A will crack the exam = 3/4

Probability that B will crack the exam = 2/3

Calculation:

Probability of both A and B solving the problem = (3/4) × (2/3) = 1/2

Probability of neither A nor B solving the problem =  ×

⇒ 1/12

Probability that only one will crack the exam =

⇒ 1 – (7/12)

⇒ 5/12

∴ The probability that only one will crack the exam is 5/12

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