Question

at a joint meeting, 78 young republicans and 97 young democrats are present to debate issues in the upcoming campus elections. on the issue of campus parking, 35% of the young democrats and 60% of the young republicans favor turning a campus green space into a parking lot. a campus newspaper reporter randomly selects a person from the group and finds that the person favors the parking space. find the probability that the person selected is a young democrat. round to two decimal places.

Explanation:

Step1: Calculate number of Young Democrats in favor

Number of Young Democrats = 97, 35% of them favor. So number of Young - Democrats in favor is $97\times0.35 = 33.95$.

Step2: Calculate number of Young Republicans in favor

Number of Young Republicans = 78, 60% of them favor. So number of Young - Republicans in favor is $78\times0.6=46.8$.

Step3: Calculate total number of people in favor

Total number of people in favor is $33.95 + 46.8=80.75$.

Step4: Calculate the probability

We want to find the probability that a person in favor is a Young Democrat. Using the formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$, here $A$ is the event of being a Young Democrat and $B$ is the event of being in favor. The probability is $\frac{33.95}{80.75}\approx0.42$.

Answer:

0.42