Question

1. the high school students who attend springfield womens academy are eligible to tryout for various teams within the athletic department. students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. many students choose to tryout for multiple teams. students have equal probabilities of being freshmen, sophomores, juniors, or seniors. what is the probability of the union of being either a freshman or junior?

0.50
0.07
0.25
0.44

Explanation:

Step1: Determine probability of each class

Since there are 4 classes (freshmen, sophomores, juniors, seniors) with equal probabilities, the probability of being a freshman ($P(F)$) or a junior ($P(J)$) is calculated by first finding the probability of each class. The total probability for all classes is 1, so each class has a probability of $\frac{1}{4} = 0.25$.

Step2: Calculate union probability (mutually exclusive)

Freshmen and juniors are mutually exclusive groups (a student can't be both a freshman and a junior at the same time). The formula for the union of two mutually exclusive events is $P(F \cup J) = P(F) + P(J)$. Substituting the values, $P(F) = 0.25$ and $P(J) = 0.25$, so $P(F \cup J) = 0.25 + 0.25 = 0.50$.

Answer:

0.50