assume your math class has 10 sophomores and 7 juniors. there are 3 female sophomores and 4 male juniors. what is the probability of randomly selecting a student who is a female or a junior
Sophomores:
10 sophomores:
3 female
male = 10 - 3 = 7
Juniors:
7 juniors
4 males
female = 7 - 4 = 3
Females:
Total Females = Female Sophomores + Female Juniors
Total Females = 3 + 3
Total Females = 6
Total Students:
Total Students = Total Sophomores + Total Juniors
Total Students = 10 + 7
Total Students = 17
We want P(female or Junior). We use the formula below to avoid duplicates:
P(female or Junior) = P(female) + P(junior) - P(female and junior)
P(female or Junior) = Total Females / Total Students + Total Juniors / Total Students - Total Female Juniors / Total Students
P(female or Junior) = 6/17 + 7/17 - 3/17
P(female or Junior) = 10/17
Sophomores:
10 sophomores:
3 female
male = 10 - 3 = 7
Juniors:
7 juniors
4 males
female = 7 - 4 = 3
Females:
Total Females = Female Sophomores + Female Juniors
Total Females = 3 + 3
Total Females = 6
Total Students:
Total Students = Total Sophomores + Total Juniors
Total Students = 10 + 7
Total Students = 17
We want P(female or Junior). We use the formula below to avoid duplicates:
P(female or Junior) = P(female) + P(junior) - P(female and junior)
P(female or Junior) = Total Females / Total Students + Total Juniors / Total Students - Total Female Juniors / Total Students
P(female or Junior) = 6/17 + 7/17 - 3/17
P(female or Junior) = 10/17