Two independent events, A and B, have probabilities P(A) = 0.4 and P(B) = 0.5. What is the… — JAMB UTME

Two independent events, $A$ and $B$ , have probabilities $P(A) = 0.4$ and $P(B) = 0.5$ . What is the probability that both event $A$ and event $B$ occur, $P(A \cap B)$ ?

Answer: 0.2

Answer

The probability that both events occur is 0.2.

For independent events, the joint probability of both events occurring simultaneously is found by multiplying their individual probabilities:

P(A \cap B) = P(A) \times P(B) = 0.4 \times 0.5 = 0.2

Step-by-Step Solution

Identify event independence and the required probability operation

Events

A

and

B

are independent, and the question requires calculating their intersection

P(A \cap B)

The problem explicitly states that the events are independent.

Apply the multiplication law for independent events

P(A \cap B) = P(A) \times P(B)

For any two independent events, the probability of both occurring together is the product of their individual probabilities.

Perform the multiplication

P(A \cap B) = 0.4 \times 0.5 = 0.2

Multiplying 0.4 by 0.5 gives 0.2.

Key Concept

Multiplication Law of Probability for Independent Events

Question

Answer

Step-by-Step Solution

Key Concept

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