Question

explore & reason
at central high school, 85% of all senior.girls attended and 65% of all senior boys
attended the spring dance. of all attendees, 20% won a prize.
a. assuming that the number of senior girls at central high school is about
equal to the number of senior boys, estimate the probability that a randomly
selected senior won a prize at the dance. explain.

b. construct arguments if you knew whether the selected student was a boy or
a girl, would your estimate change? explain.

habits of mind
look for relationships how would the probability that a senior selected at random
won a prize be different if only 60% of senior girls and 50% of senior boys attended
the dance? explain.

Explanation:

Step1: Calculate the probability of a senior girl attending and winning a prize

Let's assume the number of senior girls and senior boys is \(n\) each. The number of senior girls attending the dance is \(0.85n\). The number of senior girls attending and winning a prize is \(0.85n\times0.2 = 0.17n\)

Step2: Calculate the probability of a senior boy attending and winning a prize

The number of senior boys attending the dance is \(0.65n\). The number of senior boys attending and winning a prize is \(0.65n\times0.2=0.13n\)

Step3: Calculate the total number of seniors attending and winning a prize

The total number of seniors (girls + boys) is \(2n\). The total number of seniors attending and winning a prize is \(0.17n + 0.13n=0.3n\)

Step4: Calculate the probability

The probability \(P=\frac{0.3n}{2n}=0.15\)

Answer:

The probability that a randomly selected senior won a prize at the dance is \(0.15\)