A flight attendant looked over a list of recent passengers. The list contained passengers' Frequent Flyer status as well as the number of bags checked.Bronze status Silver status0 checked bags 3 31 checked bag 4 7What is the probability that a randomly selected passenger has bronze status given that the passenger has 1 checked bag?Simplify any fractions.
Question
A flight attendant looked over a list of recent passengers. The list contained passengers' Frequent Flyer status as well as the number of bags checked.Bronze status Silver status0 checked bags 3 31 checked bag 4 7What is the probability that a randomly selected passenger has bronze status given that the passenger has 1 checked bag?Simplify any fractions.
Solution
To solve this problem, we need to use the formula for conditional probability, which is P(A|B) = P(A ∩ B) / P(B). In this case, event A is a passenger having bronze status and event B is a passenger having 1 checked bag.
Step 1: Calculate P(A ∩ B), the probability of a passenger having bronze status and 1 checked bag.
From the table, we can see that there are 4 passengers with bronze status and 1 checked bag. The total number of passengers is 3 (bronze, 0 bags) + 3 (silver, 0 bags) + 4 (bronze, 1 bag) + 7 (silver, 1 bag) = 17 passengers. So, P(A ∩ B) = 4/17.
Step 2: Calculate P(B), the probability of a passenger having 1 checked bag.
From the table, we can see that there are 4 (bronze, 1 bag) + 7 (silver, 1 bag) = 11 passengers with 1 checked bag. So, P(B) = 11/17.
Step 3: Substitute P(A ∩ B) and P(B) into the formula for conditional probability.
P(A|B) = P(A ∩ B) / P(B) = (4/17) / (11/17) = 4/11.
So, the probability that a randomly selected passenger has bronze status given that the passenger has 1 checked bag is 4/11.
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