Question

Suppose you just purchased a digital music player and have put 13 tracks on it. After listening to them you decide that you like 3 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.

Answer 1

a)P(You like both of them)=(3/13)*(2/12)=0.0385

as probability of above event is less than 0.05 , therefore this is an unusual event

b)

P(like neither) =(10/13)*(9/12)=0.5769

c)

P( You like exactly one of them)=(10/13)*(3/12)+(3/13)*(10/12)=0.3846

with repetition allowed"

d-a) P(You like both of them)=(3/13)*(3/13)=0.0533

this is not unusual

d-b) P(like neither) =(10/13)*(10/13)=0.5917

d-c) P( You like exactly one of them)=(10/13)*(3/13)+(3/13)*(10/13)=0.3550