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The conditional probability that a Philadelphian who got the flu got a flu shot is of:
0.4375 = 43.75%.
<h3>What is Conditional Probability?</h3>Conditional probability is the probability of one event happening, considering the outcome of a previous event.
The formula is presented as follows:
In which each probability in the formula is described as follows:
- P(B|A) is the probability of the event B happening, given that the event A happened.
is the probability of both the events A and B happening.
- P(A) is the probability of the event A happening.
In the context of this problem, the events are described as follows:
- Event A: Got the flu.
- Event B: Got the flu shot.
The probability of people who got the flu is obtained as follows:
- 2% of 70%. (got the shot).
- 6% of 30%. (did not get the shot).
Hence:
P(A) = 0.02 x 0.7 + 0.06 x 0.3 = 0.032.
The probability of both getting the flu and the shot is:
P(A and B) = 0.02 x 0.7 = 0.014.
Hence the conditional probability that a Philadelphian who got the flu got a flu shot is calculated applying the conditional probability formula as follows:
P(B|A) = P(A and B)/P(A) = 0.014/0.032 = 0.4375 = 43.75%.
More can be learned about conditional probability at brainly.com/question/14398287
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