If the probability of event A is 0.4 and the probability of event B is 0.5, what is the probability of both A and B occurring if they are independent?
Practice Questions
1 question
Q1
If the probability of event A is 0.4 and the probability of event B is 0.5, what is the probability of both A and B occurring if they are independent?
0.2
0.4
0.5
0.9
For independent events, P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.
Questions & Step-by-step Solutions
1 item
Q
Q: If the probability of event A is 0.4 and the probability of event B is 0.5, what is the probability of both A and B occurring if they are independent?
Solution: For independent events, 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 events A and B are independent, meaning the occurrence of one does not affect the other.
Step 4: Use the formula for independent events: 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 result: 0.4 * 0.5 = 0.2.
Step 7: Conclude that the probability of both A and B occurring is 0.2.
