Judy applied to ten colleges. Each college can either accept (A) or reject (R) her application. Define X as the number of colleges Judy is accepted into. Assume that the number of colleges she is accepted into is distributed binomial. The probability of acceptance at a college is .40 and is the same at all ten colleges.    Judy thinks that because the probability of getting into each college is .40, she has a .40 probability of getting into 4 out of ten colleges. What is the actual probability that Judy is accepted into 4 colleges? Round to two decimal places.

College Algebra
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ISBN:9781337282291
Author:Ron Larson
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Chapter8: Sequences, Series,and Probability
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Judy applied to ten colleges. Each college can either accept (A) or reject (R) her application. Define X as the number of colleges Judy is accepted into. Assume that the number of colleges she is accepted into is distributed binomial. The probability of acceptance at a college is .40 and is the same at all ten colleges. 

 

Judy thinks that because the probability of getting into each college is .40, she has a .40 probability of getting into 4 out of ten colleges. What is the actual probability that Judy is accepted into 4 colleges? Round to two decimal places. 

Expert Solution
Step 1

Suppose X be the number of colleges Judy is accepted into.

Assume that the number of colleges she is accepted into is distributed binomial.

The probability of acceptance at a college is 0.40 i.e. p=0.40.

and is the same at all ten colleges. 

The number of selected colleges are n=10.

i.e. X~B(n=10, p=0.40)

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