The probability of a student belonging to a club or working part-time can be calculated by finding the probabilities of each event individually and their intersection. The final probabilities are: belonging to a club: 0.40, working part-time: 0.50, belonging to a club and working part-time: 0.15, belonging to a club given working part-time: 0.30, belonging to a club or working part-time: 0.75.
Probability of a Student Belonging to a Club or Working Part-Time
Find the probability that the student belongs to a club by summing the probabilities in C, which is 0.40.
Find the probability that the student works part-time by summing the probabilities in PT, which is 0.50.
The probability that the student belongs to a club AND works part-time is the intersection of the probabilities, which is 0.15.
Using the formula for conditional probability, calculate the probability that the student belongs to a club given that the student works part-time by dividing the intersection probability by the probability of working part-time.
The probability that the student belongs to a club OR works part-time is found by summing the probabilities of belonging to a club and working part-time, and subtracting the intersection probability to avoid double-counting.
Final probability:
a. Probability the student belongs to a club: 0.40
b. Probability the student works part-time: 0.50
c. Probability the student belongs to a club AND works part-time: 0.15
d. Probability the student belongs to a club given that the student works part-time: 0.30
e. Probability the student belongs to a club OR works part-time: 0.40 + 0.50 - 0.15 = 0.75