Question

Suppose on a CD, you like 8 out of 19 songs. If you randomly select four songs to be played once, what is the probability that

(a) You like 3 of the songs out of the 4? Enter your answer rounded to two decimals.

(b) You like the first two songs and then dislike the second two songs, in that order? Enter your answer rounded to two decimals.

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Total number of songs = 19

Number of songs you like = 8

Number of songs you do not like = 19 - 8 = 11

a) P(you like 3 songs put of 4) = Number of ways to select 3 songs you like x Number of ways to select 1 song you dont like / Number of ways to select any 4 songs

= 8C3 x 11C1 / 19C4

= 56 x 11 / 3876

= 0.16

b) P(you like the first two songs and then dislike the second two songs, in that order) = 8/19 x 7/18 x 11/17 x 10/16

= 0.07