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Suppose you just purchased a digital music player and have put 13 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your​ player, each of the 13 songs is played once in random order. Find the probability that among the first two songs played ​(a) You like both of them. Would this be​ unusual? ​(b) You like neither of them. ​(c) You like exactly one of them. ​(d) Redo​ (a)-(c) if a song can be replayed before all 13 songs are played.

 Apr 21, 2020
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You like 2 of 13 songs.

 

a)  Getting both of the songs (no repeats):  (2/13) x (1/12)  =

b)  Getting neither song (no repeats):  (11/13) x (10/12)  =

c)  Getting one of them, in either order (no repeats):  (2/13) x (11/12)  +  (11/13) x (2/12)  = 

 

a)  Getting both of the songs (repeats allowed):  (2/13) x (2/13)  =

b)  Getting neither song (repeats allowed):  (11/13) x (11/13)  =

c)  Getting one of them, in either order (repeats allowed):  (2/13) x (11/12)  +  (11/13) x (2/12)  = 

 Apr 22, 2020

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