Question

this year the cdc reported that 30% of adults received their flu shot. of those adults who received their flu shot, 20% still got the flu. of those who did not receive the flu shot, 65% got the flu. whats the probability that a randomly selected adult got the flu? enter your answer as a decimal to the ten thousandths place.

Explanation:

Step1: Calculate probability for adults with flu shot and flu

Multiply the probability of getting a flu shot ($0.3$) by the probability of getting flu given a flu shot ($0.2$):
$0.3\times0.2 = 0.06$

Step2: Calculate probability for adults without flu shot and flu

Multiply the probability of not getting a flu shot ($0.7$) by the probability of getting flu given no flu shot ($0.65$):
$0.7\times0.65=0.455$

Step3: Find total probability of getting flu

Add the two probabilities from Step1 and Step2:
$0.06 + 0.455=0.515$

Answer:

$0.5150$