Before graduating this year, a senior homeroom was given a survey. Of those surveyed, 24% felt they learned better at home. Of this group, 80% said they plan on taking an online course in college. Of the students who felt they did not learn better at home, 40% said they plan on taking an online course in college Part A
What is the probability a person who does not plan on taking an online course felt they learned better at home?

A : 2/21
B : 24/125
C : 38/125
D : 19/31
E :None of these

Part B
What is the probability a person who does plan on taking an online course felt they did not learn better at home?

A : 2/21
B : 24/125
C : 38/125
D : 19/31
E : None of these

(A) The correct option is (A).

(B) The correct option is (E).

Step-by-step explanation:

The events can be defined as follows:

X =  students felt they learned better at home

Y = students plan on taking an online course in college

The information provided is:

P (X) = 0.24

P (Y|X) = 0.80

P (Y|X') = 0.40

The Bayes' theorem states that the conditional probability of an event E given that another event A has already occurred is:

(A)

Compute the probability a person who does not plan on taking an online course felt they learned better at home as follows:

Use the Bayes' theorem.

Thus, the probability a person who does not plan on taking an online course felt they learned better at home is 0.095 or 2/21.

(B)

Compute the probability a person who does plan on taking an online course felt they did not learn better at home as follows:

Thus, the probability a person who does plan on taking an online course felt they did not learn better at home is 0.905.

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step-by-step explanation: