Question

1. You have downloaded 20 new songs onto your phone as shown in the table. Artist Number of Songs A Tribe Called Red 3 Drake 8 The Weeknd 7 Alessia Cara 2 Assuming order does not matter, if you randomly play 8 from your new list of downloaded songs, what is the probability, without evaluating, that you will hear: a. no A Tribe Called Red songs? b. exactly three Drake songs or exactly four Drake songs? c. two songs from each artist? d. at least one The Weeknd song?

Answer 1

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

Number of ways to select 8 songs from total 20 = 20C8

= 125,970

a) P(no A Tribe Called Red songs) = All songs are selected from 17 songs that are not A Tribe Called Red songs

= 17C8/20C8

= 0.1930

b) P(exactly 3 Drake songs or exactly 4 Drake songs) = P(3 Drake songs and 5 other songs) + P(4 Drake songs and 4 other songs)

= 8C3x12C5/20C8 + 8C4x12C4/20C8

= 0.3521 + 0.2751

= 0.6272

c) P(two songs from each artist) = (3C2 x 8C2 x 7C2 x 2C2)/20C8

= 0.0140

d) P(at least one The Weekend song) = 1 - P(all songs are not The Weekend songs)

= 1 - 13C8/20C8

= 1 - 0.0102

= 0.9898