Question

harper asked the juniors and seniors at her school whether the drama club should perform the spring play in march, april, or may this year.

	march	april	may	total
seniors	28	52	24	104
total	71	89	56	216

rounded to the nearest hundredth, what is the probability that a randomly selected student from harpers survey is a junior given that they chose may?
0.15 0.29 0.52 0.57

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 the table, if $A$ is the event of being a junior and $B$ is the event of choosing May, then $P(A\cap B)$ is the probability of being a junior and choosing May, and $P(B)$ is the probability of choosing May.

Step2: Find $P(A\cap B)$ and $P(B)$

The number of juniors who chose May is 32, and the total number of students is 216. So $P(A\cap B)=\frac{32}{216}$. The number of students who chose May is 56, so $P(B)=\frac{56}{216}$.

Step3: Calculate $P(A|B)$

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{32}{216}}{\frac{56}{216}}=\frac{32}{56}\approx0.57$.

Answer:

0.57