Question

select the correct answer. the results of a survey about the ages of students at a local college are shown below. if a student is randomly selected, which event is most likely? p(18 - 22 | male) p(male | 30+) p(18 - 22 | female) p(female | 23 - 29) table: male female total 18 - 22 350 325 675 23 - 29 100 125 225 30+ 50 30 80 total 500 480 980

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequency, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.

Step2: Calculate $P(18 - 22|male)$

$n(18 - 22\cap male)=350$, $n(male)=500$. So $P(18 - 22|male)=\frac{350}{500}=0.7$.

Step3: Calculate $P(male|30 +)$

$n(male\cap30 +)=50$, $n(30 +)=80$. So $P(male|30 +)=\frac{50}{80}=0.625$.

Step4: Calculate $P(18 - 22|female)$

$n(18 - 22\cap female)=325$, $n(female)=480$. So $P(18 - 22|female)=\frac{325}{480}\approx0.677$.

Step5: Calculate $P(female|23 - 29)$

$n(female\cap23 - 29)=125$, $n(23 - 29)=225$. So $P(female|23 - 29)=\frac{125}{225}\approx0.556$.

Since $0.7$ is the largest among the calculated conditional - probabilities, the event $P(18 - 22|male)$ is most likely.

Answer:

$P(18 - 22|male)$