Vanessa has 16 songs on a Classic Rock CD. Six of the songs are by the Beatles, 4 are by the Rolling Stones, 4 are by the Who, and 2 are by the Doors. Vanessa plays the CD. She selects a setting that randomly chooses songs to play.
Find the probability of each event:
a) The first 3 songs played are by the Beatles.
b) The first 2 songs played are by the Rolling Stones and the next 2 songs are by the Beatles.
c) The first 2 songs played are by the Doors, and the next song played is either by the Beatles or the Rolling Stones.

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joaobezerra joaobezerra · Answer 1 · 2022-06-24T19:24:01+02:00

Using it's concept, it is found that the probabilities are given as follows:

a) 0.0527 = 5.27%.

b) 0.0088 = 0.88%.

c) 0.0098 = 0.98%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Item a:

6 out of 16 songs are of the Beatles, hence the probability of a single music being from the Beatles is:

[tex]pB = \frac{6}{16} = \frac{3}{8}[/tex]

Of three musics, the probability is:

[tex]p = \left(\frac{3}{8}\right)^3 = 0.0527[/tex]

Item b:

For the Rolling stones, the probability is:

[tex]pR = \frac{4}{16} = \frac{1}{4}[/tex]

For the four musics, the probability is:

[tex]p = \left(\frac{1}{4}\right)^2 \times \left(\frac{3}{8}\right)^2 = 0.0088[/tex]

Item c:

For the doors, the probability is:

[tex]pD = \frac{2}{16} = \frac{1}{8}[/tex].

For Beatles or Rolling stones, the probability is:

[tex]pBR = \frac{10}{16} = \frac{5}{8}[/tex]

For the three musics, the probability is:

[tex]p = \left(\frac{1}{8}\right)^2 \times \frac{5}{8} = 0.0098[/tex]

More can be learned about probabilities at https://brainly.com/question/14398287

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