If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?

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Q: If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?

Solution: P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

Steps: 7

Step 1: Understand that the probability of event A is 0.4.
Step 2: Understand that the probability of event B is 0.5.
Step 3: Know that if two events are independent, the probability of both events happening together is found by multiplying their probabilities.
Step 4: Write the formula for the probability of both events A and B occurring: P(A and B) = P(A) * P(B).
Step 5: Substitute the values into the formula: P(A and B) = 0.4 * 0.5.
Step 6: Calculate the multiplication: 0.4 * 0.5 = 0.2.
Step 7: Conclude that the probability of both events A and B occurring is 0.2.