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.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

21/58.

hope to be marked brainliest