Suppose a CD you just purchased has 10 tracks After listenin

Suppose a CD you just purchased has 10 tracks. After listening to the CD you decide that you like 4 of the songs. With the Random Feature on your CD player, each of the 7 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 10 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