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October 13th, 2013, 08:14 PM   #1
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Randomly playing songs probability

Suppose a compact disc you just purchased has 13 tracks. After listening to the CD, you decide that you like 5 of the songs. The random feature on your CD player will play each of the 13 songs once in a random order. Find the probability that among the first 4 played
(a) you like 2 of them;
(b) you like 3 of them;
(c) you like all 4 of them
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October 14th, 2013, 05:14 PM   #2
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Re: Randomly playing songs probability

Quote:
Originally Posted by Moy510
Suppose a compact disc you just purchased has 13 tracks. After listening to the CD, you decide that you like 5 of the songs. The random feature on your CD player will play each of the 13 songs once in a random order. Find the probability that among the first 4 played
(a) you like 2 of them;
(b) you like 3 of them;
(c) you like all 4 of them
Since the CD player plays "each of the 13 songs once there is no repetition.

(c) is easiest- there are 13 songs and you like 5 of them. The probability the first is a song you like is 5/13. Assuming that happens, there are now 12 songs, 4 of which you like. The probability the next is a song you like is 4/12. After that there are 11 songs, 3 of which you like. The probability the next is a song you like is 3/11. Finally, there are 10 songs, 2 of which you like. The probability the last song is a song your like is 2/12. The probability all four are songs you like is (5/13)(4/12)(3/11)(2/10).

Now, back to (a). As before, the probability the first song is one you like is 5/13 and the probability the second song is one you like is 4/12. As before, there are now 11 songs left and you like 2 of them. The probability the third song is one you don't like is 9/11. Now there are 10 songs left but you still like 2 of them. The probability the fourth song is one you don't like is 8/10. The probability the first four songs are two that you like, two that you don't like, in that order, is (5/13)(4/13)(9/11)(8/10). If you look at things like "first song you don't like, next two you do, fourth song you don't" you will see that you get exactly the same answer! (Different fractions but same denominators and same numerators in different order.) So you just need to multiply by the number of orders. How many orders are there of "AABB"?
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