Question

Thirty-two percent of students take fewer than 4 courses per term. Seventy-five percent of students taking fewer than 4 courses per term work full-time. Thirty-five percent of students work full-time. What percentage of students take at least 4 courses and do not work full-time?

Answer 1

let event A be that student take fewer than 4 courses per term and event B be that student work full-time

According to question, P(A) = 32% = 32/100 = 0.32 and P(B) = 35% = 35/100 = 0.35

P(B|A) = 75% = 75/100 = 0.75

By conditional probability formula, P(A and B) = P(B|A)*P(A) = 0.75*0.32 = 0.24

Find P(A or B) using general addition rule

P(A or B) = P(A) + P(B) - P(A and B)

= 0.32 + 0.35 - 0.24

= 0.43

We know that P(not A and not B) = 1 - P(A or B) = 1 - 0.43 = 0.57

Convert to %, 0.57*100 = 57%

Therefore, 57 percentage of students take at least 4 courses and do not work full-time