Question

1. the high school students who attend washington preparatory academy choose their elective classes according to their majors. students are 37% likely to major in performing arts; 43% likely to choose science and technology; 82% likely to major in business and management; and 63% likely to select humanities. many students choose multiple majors. for example, some science and technology students also major in business and management because they want to be managers in technical companies. students have equal probabilities of being freshmen, sophomores, juniors, or seniors. what is the probability of the intersection of being a junior and a business and management major? 0.87 0.25 0.82 0.21

Explanation:

Step1: Determine probability of being a junior

There are 4 grade levels (freshmen, sophomores, juniors, seniors) with equal probabilities. So \( P(\text{junior})=\frac{1}{4} = 0.25\).

Step2: Determine probability of Business and Management major

\( P(\text{Business and Management}) = 0.82\).

Step3: Assume independence (since grade and major choice are likely independent)

For independent events, \( P(A\cap B)=P(A)\times P(B)\). Here, \( A=\text{junior}\), \( B = \text{Business and Management}\). So \( P(\text{junior}\cap\text{Business and Management})=0.25\times0.82 = 0.205\approx0.21\).

Answer:

0.21