(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

You are a member of a class of 18 students. A bowl contains 18 chips: 1 blue and 17 red. Each student is to take 1 chip from the bowl without replacement. The student who draws the blue chip is guaranteed an A for the course.

a)If you have the choice of drawing first, fifth, or last, which position would you choose? Justify you choice on the basis of probability.

b) Suppose the bowl contains 2 blue and 16 red chips. Which position would you now choose?

2. Relevant equations

I use a combinatorics formula that I will show on solution.

3. The attempt at a solution

I said that the 1st person has a simple chance of winning: 1/18

The 5th person, however, has to wait for 4 others to select the wrong chip so:

[(1C0)(17C4)/(18C4)] * (1/14). This gives me the probability of 1/18 though.

And the last person has to wait for 17 people to pick the wrong chip:

[(1C0)(17C17)/(18C17)]*(1/1). This give me the probability of 1/18 as well.

So I said I would like to be the 5th person for another reason. Last person has an unlikely chance that the people before him would not pick the blue chip (1/18). The 1st person has a (1/18) shot in the dark. While there is a 7/9 chance that the other people will pick the wrong chip. Leaving him a 1/14 chance of picking the blue chip.

I will pick up on part b later if the first part is correct. Does what I did make sense?

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# A conditional probability question on picking out chips from a bowl.

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