Mathematics

Mathematics

Problem

Two events A and B each have probability 0.50. Which of the following values of P(A∩B)P(A\cap B) would imply that A and B are independent? a) 0.000.00 b) 1.001.00 c) 0.250.25 d) 0.500.50
Intuitive explanation

Independence means that knowing one event happened tells you nothing about the other—mathematically, P(A∩B)=P(A)⋅P(B)P(A \cap B) = P(A) \cdot P(B). Since both events have probability 0.50, you just need to multiply those probabilities together to find what the intersection probability must be if they're independent. That single value is your answer.

Intuitive explanation

Independence means that knowing one event happened tells you nothing about the other—mathematically, P(A∩B)=P(A)⋅P(B)P(A \cap B) = P(A) \cdot P(B). Since both events have probability 0.50, you just need to multiply those probabilities together to find what the intersection probability must be if they're independent. That single value is your answer.

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