High School

Suppose the probability of beating your brother at checkers is 0.54, the probability of beating your sister at checkers is 0.48, and the probability of beating both your sister and brother at checkers is 0.33.

What is the probability you beat your sister given that you beat your brother at checkers?

Answer :

Answer:

1.55

Step-by-step explanation:

Final answer:

To calculate the probability of beating your sister given that you have beaten your brother, we use the formula for conditional probability, which is approximately 61.11%.

Explanation:

To find the probability that you beat your sister given that you have beaten your brother, we pertain to the concept of conditional probability. The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of event A occurring given event B has occurred.

In this scenario, event A is beating your sister and event B is beating your brother. The given probabilities are P(A) = 0.48, P(B) = 0.54, and P(A and B) = 0.33. Using the formula, we calculate P(A|B) as follows: P(A|B) = P(A and B) / P(B) = 0.33 / 0.54.

Therefore, the probability that you beat your sister given that you beat your brother is about 0.6111, or 61.11%.