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.
The probability that a randomly selected student from the class is a male or a junior = 33/40 or 0.825
The probability of an event is a fractional value representing the chance of the event taking place. The probability of event A can be determined by the ratio of the number of outcomes favorable to event A, to the total number of outcomes.
We are informed that in a statistics class, there are 22 juniors and 18 seniors. Of the juniors, 12 are females. Of the seniors, 11 are males.
We are asked to find the probability that a randomly selected student from the class is a male or a junior.
To find the probability, we first need to find the number of juniors or males in the class.
The number of juniors = 22.
The number of males = (22-12) + 11 = 10 + 11 = 21 {Taking (22 - 12) as there are 12 females among the 22 juniors}
Now, we have counted male juniors in both cases.
The number of male juniors = 22 - 12 = 10.
∴ Total number of favorable outcomes = The number of juniors + The number of males - The number of male juniors = 22 + 21 - 10 = 33.
Total number of outcomes = Total students = 22 + 18 = 40
∴ The probability that a randomly selected student from the class is a male or a junior = Total number of favorable outcomes/Total number of outcomes = 33/40 or 0.825
Learn more about the probability of an event at
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