Question

the data on the right represent the number of traffic fatalities by seat location and sex. determine p(female) and p(female|passenger). are the events \female\ and \passenger\ independent? (round to three decimal places as needed.) determine p(female|passenger). p(female|passenger)=0.264 (round to three decimal places as needed.) are the events \female\ and \passenger\ independent? a. yes. the occurrence of the event \passenger\ affects the probability of the event \passenger.\ b. yes. the occurrence of the event \passenger\ does not affect the probability of the event \female.\ c. no. the occurrence of the event \passenger\ affects the probability of the event \female.\ d. no. the occurrence of the event \passenger\ does not affect the probability of the event \female.\

Explanation:

Step1: Calculate P(female)

The total number of females is 17,989 and the total number of people is 57,268. So $P(\text{female})=\frac{17989}{57268}\approx 0.314$.

Step2: Recall the concept of independent events

Two events $A$ and $B$ are independent if $P(A|B)=P(A)$. Here $A$ is the event "female" and $B$ is the event "passenger". We are given $P(\text{female}|\text{passenger}) = 0.264$ and we found $P(\text{female})\approx0.314$. Since $P(\text{female}|\text{passenger})
eq P(\text{female})$, the events are not independent. The occurrence of the event "passenger" affects the probability of the event "female".

Answer:

$P(\text{female})\approx0.314$
C. No. The occurrence of the event "passenger" affects the probability of the event "female."