Answer :
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%.
