Question

In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females and 12 of the juniors are males. If a student is selected at random, find the probability of selecting the following.
a. A junior or a female
b. A senior or a female
c. A junior or a senior

Answer 1

Answer:

a) 0.857

b) 0.571

c) 1

Step-by-step explanation:

Based on the data given, we have

• 18 juniors
• 10 seniors
• 6 female seniors
• 10-6 = 4 male seniors
• 12 junior males
• 18-12 = 6 junior female
• 6+6 = 12 female
• 4+12 = 16 male
• A total of 28 students

The probability of each union of events is obtained by summing the probabilities of the separated events and substracting the intersection. I will abbreviate female by F, junior by J, male by M, senior by S. We have

• P(J U F) = P(J) + P(F) - P(JF) = 18/28+12/28-6/28 = 24/28 = 0.857

• P(S U F) = P(S) + P(F) - P(SF) = 10/28 + 12/28 - 6/28 = 16/28 = 0.571

• P(J U S) = P(J) + P(S) - P(JS) = 18/28 + 10/28 - 0 = 1

Note that a student cant be Junior and Senior at the same time, so the probability of the combined event is 0. The probability of the union is 1 because every student is either Junior or Senior.