P(A) = 0.50, P(B) = 0.40, and P(A and B) = 0.15. What is P(A or B)?
A. 0.65
B. 0.90
C. 0.75
D. 0.55
Answer (1)
The problem provides P ( A ) , P ( B ) , and P ( A \t an d B ) .
The formula for P ( A \t or B ) is P ( A ) + P ( B ) − P ( A \t an d B ) .
Substitute the given values into the formula: 0.50 + 0.40 − 0.15 .
Calculate the result: 0.75 .
Explanation
Understand the problem and provided data We are given the probabilities of events A and B, as well as the probability of both A and B occurring. We need to find the probability of either A or B occurring (or both).
Recall the formula for P(A or B) The formula for the probability of A or B is: P ( A \t or B ) = P ( A ) + P ( B ) − P ( A \t an d B ) This formula accounts for the overlap between the two events, ensuring that we don't count the intersection twice.
Substitute the given values We are given: P ( A ) = 0.50 P ( B ) = 0.40 P ( A \t an d B ) = 0.15 Substitute these values into the formula: P ( A \t or B ) = 0.50 + 0.40 − 0.15
Calculate the result Now, we perform the calculation: P ( A \t or B ) = 0.90 − 0.15 = 0.75 So, the probability of A or B occurring is 0.75.
State the final answer The probability of A or B occurring is 0.75.
Examples
Understanding the probability of either event A or B occurring is useful in many real-world scenarios. For example, in marketing, event A could represent a customer clicking on an ad, and event B could represent a customer making a purchase. Knowing the probability of a customer either clicking on an ad or making a purchase helps businesses optimize their marketing strategies. Another example is in weather forecasting, where event A could be the probability of rain and event B could be the probability of snow. The probability of either rain or snow helps people prepare for the weather conditions. In this case, the probability of A or B is calculated as: P ( A or B ) = P ( A ) + P ( B ) − P ( A and B ) .
