Dr. Skullcruncher gives his class ten essay questions in advance, and promises t

Question

Dr. Skullcruncher gives his class ten essay questions in advance, and promises that he will select two of them at random for their next exam. How many different possible pairs of questions are there? The order in which he selects the questions does not matter.

Select one:

100

36

45

2,598,260

90

Of the ten questions Dr. Skullcruncher gave you in advance, you know you are totally unprepared to answer 8 of them.

How many different pairs could the professor select just from this set of 8 questions?

Continuing, suppose you only have to answer one of the two questions Professor Skullcruncher picks.

What's the probability that both of the questions he picks just happen to be from the 8 questions you were unprepared for? Give your answer to at least two decimal places.

Explanation / Answer

These question has three parts.

1) Selecting two questions out of 10 = 10C2 = 45

2) Selecting two questions out of 8 unprepared = 28

3) P(Both questions from unprepared)

To find this probbility, we need to divide the 2nd answer by 1st answer i.e.

P(Both questions from unprepared)

= (Selection from 8 unprepaed questions) / (Selection from all 10 questions)

= 28 / 45

= 0.62 (Rounded off to two decimal places)

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