Question 998452: Of the professors at NSU, 44% are female. If you sign up for 5 classes next semester, find the probability that you will get all female professors.
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Problem:
44% of professors at NSU are female.
Find probability of having all female professors if 5 classes are chosen randomly.
Solution:
This problem can be solved using binomial distribution because:
1. number of steps in experiment is known (n=5)
2. probability of choosing a class taught by female professor is constant (p=0.44) since each professor could teach multiple courses.
3. the choice of classes is assumed random (otherwise the probability is 1)
4. each step (choice of each class) is a Bernoulli experiment, i.e. with two possible outcomes (male or female professor only)
The probability of choosing all 5 classes taught by female professor(s) is therefore calculated using the binomial distribution with parameters
n=5 (number of steps)
p=0.44
r=5 (5 successes)
P(5,5,0.44)=C(5,5)*(0.44)^5*(1-0.44)^(5-5)
=1*(0.44)^5*1
=0.01649
Answer: the probability of randomly choosing all 5 classes taught by female professors at NSU is 0.01649
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