Question

For two events A and B, a student calculates that P(A and B) = 0.46 and P(B|A) = 0.31. Explain how you can tell that the student made a mistake.

Answer 1

Conditional probability formula is:P ( A and B ) = P ( A ) · P ( B / A )0.46 = P ( A ) · 0.31P ( A ) = 0.46 : 0.31P ( A ) = 1.48And this is impossible because 0 ≤ P ( A ) ≤ 1The student obviously made a mistake.