Question

each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. the results are shown in the contingency table. find the probability that the student preferred afternoon classes given he or she is a junior. round to the nearest thousandth. when do you prefer to take classes? freshman sophomore junior senior morning 19 2 6 16 afternoon 17 3 13 15 evening 8 14 9 7

Answer 1

0.464

Explanation:

You want the probability that a student prefers afternoon classes, given that the student is a junior.

Probability

The conditional probability can be found using the formula ...

P(A|J) = P(A&J)/P(J)

For the values on the right, we can use numbers of students. This gives ...

P(A|J) = 13/(6+13+9) = 13/28 ≈ 0.464

The probability that a student prefers afternoon classes given they are a junior is about 0.464.

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Additional comment

We can use numbers of students in the above calculation because the corresponding probability is that number divided by the total number of students. That "divided by" factor is common to numerator and denominator, so cancels. This simplifies the calculation.

We used A|J to signify "prefers afternoon" given "is a junior".

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