If the probability of event A is 0.2 and the probability of event B is 0.5, what
Practice Questions
Q1
If the probability of event A is 0.2 and the probability of event B is 0.5, what is the probability of either A or B occurring if A and B are independent?
0.7
0.6
0.5
0.4
Questions & Step-by-Step Solutions
If the probability of event A is 0.2 and the probability of event B is 0.5, what is the probability of either A or B occurring if A and B are independent?
Step 1: Identify the probability of event A, which is given as 0.2.
Step 2: Identify the probability of event B, which is given as 0.5.
Step 3: Since A and B are independent, calculate the probability of both A and B occurring together (P(A and B)). This is done by multiplying their probabilities: P(A and B) = P(A) * P(B) = 0.2 * 0.5.
Step 4: Calculate P(A and B): 0.2 * 0.5 = 0.1.
Step 5: Use the formula for the probability of either A or B occurring: P(A or B) = P(A) + P(B) - P(A and B).
Step 6: Substitute the values into the formula: P(A or B) = 0.2 + 0.5 - 0.1.
Step 7: Calculate the result: 0.2 + 0.5 = 0.7, then 0.7 - 0.1 = 0.6.
Step 8: The final answer is that the probability of either A or B occurring is 0.6.
Probability of Independent Events – Understanding how to calculate the probability of either of two independent events occurring using the formula P(A or B) = P(A) + P(B) - P(A and B).
Complementary Events – Recognizing that the probability of both events occurring together (P(A and B)) is calculated as the product of their individual probabilities when they are independent.
