A professor gave her students six essay questions from which she will select three for a test. A student has time to study for only three of these questions. What is the probability that, of the questions studied,

(a) at least one is selected for the test?

(b) all three are selected?

(c) exactly two are selected?

Answer:

Step 1 of 4:

Given that, a professor gave her students six essay questions from which she will select three for a test. A student has time to study for only three of these questions.

Step 2 of 4:

The aim is to find the probability that, of the questions studied,

a). To find the probability that at least one is selected for the test.

Let ‘x’ be the number of chosen studied questions.

The number of not studied questions in the sample is ways.

The number of studied questions in the sample is ways.

And selecting 3 questions from 6 questions is ways.

Therefore,

P(at least one selected) = 1- P(none of them selected)

= 1-

= 1-

=

Therefore, the probability that at least one is selected for the test is 0.95.