# Stats 213 Problem 2?

An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection of 9 of them. If a student has figured out how to do 16 of the problems, what is the probability the he or she will answer correctly

(a) all 9 problems?

(b) at least 8 problems?

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• Anonymous
1 month ago

So if the student has figured out how to do 16 out of 18 problems, the probability that he will answer 9 of them correct is 4/17, and the probability that he will answer at least 8 of them correct is 13/17.

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This can be treated as an instance of the

Hypergeometric distribution

See Wikipedia Article

https://en.wikipedia.org/wiki/Hypergeometric_distr...

= ( ( K over k ) ( (N-K) over (n-k) ) /

( N over n )

over mean combination

where is N is total number of original items  = 18

K is the number of original which meet passing

requirement

K = 9

n is the number of item to be chosen from the

group of N = 9

k is how of n which meet passing requirement

(k =9 in one of your questions and k =8 in part of your

other question.)

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• (a)

F: a certain problem is figured out (there are 16 F's)

N: a certain problem is not figured out (there are 2 N's)

Total number of ways to randomly choose 9 problems for 18

= ₁₈C₉

= 48620

To answer all 9 problems correctly, choose 9F (from 16) in the quiz.

Number of ways

= ₁₆C₉

= 11440

= P(all 9 problems correct)

= 11440/48620

= 4/17

====

(b)

To answer 8 problems correctly, choose 8F from (16) and 1N (from 2) in the quiz.

= ₁₆C₈ × ₂C₁

= 25740

P(8 problems correct)

= 25740/48620

= 9/17

P(at least 8 problems correct)

= P(all 9 problems correct) + P(8 problesm correct)

= (4/17) + (9/17)

= 13/17

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• (16/18) * (15/17) * (14/16) * (13/15) * (12/14) * (11/13) * (10/12) * (9/11) * (8/10) =>

(1/18) * (1/17) * (16/16) * (15/15) * (14/14) * (13/13) * (12/12) * (11/11) * (10/10) * 9 * 10 =>

(9/18) * (10/17) * 1 * 1 * 1 * 1 * 1 * 1 * 1 =>

(1/2) * (10/17) =>

5/17

You have a 5/17 chance of getting all 9 correct

(16/18) * (15/17) * ... * (9/11) * (2/10) =>

(16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 2) / (18 * 17 * 16 * 15 * ... * 10) =>

(9 * 2) / (18 * 17) =>

1/17

You have a 1/17 chance of getting 8 correct

1/17 + 5/17 = 6/17

You have a 6/17 chance of getting at least 8 correct

• Lv 5
1 month agoReport

That is incorrect.

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