Suppose a CD you just purchased has 15 tracks After listenin

Suppose a CD you just purchased has 15 tracks. After listening to the CD you decide that you like 2 of the songs. With the Random Feature on your CD player, each of the 15 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 15 songs are played.

ROUND TO THREE DECIMALS AS NEEDED

Solution

a) there are 15 songs and you like 2 of them. The probability the first is a song you like is 2/15. Assuming that happens, there are now 14 songs, 1 of which you like. The probability the next is a song you like is 1/14. . The probability both are songs you like is

(2/15)*(1/14) =0.0095

Yes it is unusual.

b) p = (13/15)*(12/14) = 0.743

c) p= (1/15)*(13/14) + (13/15)*(2/14) = 0.062 + 0.124 = 0.0186

d) both:

(2/15)*(2/15) =0.0178

Neither:

p = (13/15)*(13/15) = 0.751

Exactly one :

p= (2/15)*(13/15) + (13/15)*(2/15) = = 0.2311