According to a recent survey, the probability that the driver in a fatal vehicle accident is female (event $F$ ) is 0.2932 . The probability that the driver is 24 years old or less (event A) is 0.1774 . The probability that the driver is female and is 24 years old or less is 0.0514 . Answer parts (a) through (d) below.
(a) Find the probability of FUA.
$P(F \cup A)=\square($ Round to four decimal places as needed. $)$
Answer
Thus, the probability of event F union A is \(\boxed{0.4192}\)
Step 1 ：We are given that the probability that the driver in a fatal vehicle accident is female (event F) is 0.2932, the probability that the driver is 24 years old or less (event A) is 0.1774, and the probability that the driver is female and is 24 years old or less is 0.0514.
Step 2 ：We are asked to find the probability of the union of two events, F and A. The formula for the probability of the union of two events is given by: \(P(F \cup A) = P(F) + P(A) - P(F \cap A)\)
Step 3 ：Substituting the given values into the formula, we get \(P(F \cup A) = 0.2932 + 0.1774 - 0.0514\)
Step 4 ：Solving the above expression, we find that \(P(F \cup A) = 0.4192\)
Step 5 ：Thus, the probability of event F union A is \(\boxed{0.4192}\)
