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Please HELP! Probability & Counting methods

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Please HELP! Probability & Counting methods

by rafodr » Wed Sep 09, 2009 11:49 am
Q: There are 8 disks in a container that are numbered 23, 24, 25, 26, 28, 29, 30, and 31. 4 disks are randomly removed from the container, one after the other, without replacement. Then a list of 5 numbers containing the 4 numbers on the disks selected, together with the number 27 will be made. What is the probability that 27 is the median of the list of 5 numbers?

A) 2/5
B) 17/35
C) 1/2
D) 18/35
E) 5/9
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by bharathh » Wed Sep 09, 2009 12:50 pm
There are 8 disks. Total # of ways to choose 4 disks = 8C4 = 70 ways

For 27 to be the median, there need to be 2 numbers less than 27 and 2 numbers more than 27.

There are 4 numbers less than 27 and 4 numbers more than 27.

There are 4C2 ways to choose 2 numbers less than 27 and more than 27. Since we want both to happen,

4C2 * 4C2 = 6 * 6 = 36

Probability = 36/70 = 18/35
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