Question

2. Last year, 70% of 1 million Philadelphians got their flu shots. About 2% of people who got

Answer 1

The conditional probability that a Philadelphian who got the flu got a flu shot is of:

0.4375 = 43.75%.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering the outcome of a previous event.

The formula is presented as follows:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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.

• $P(A \cap B)$ 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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