Question

Charles has four songs on a playlist. Each song is by a different artist. The artists are Bryan Adams, Stevie Wonder, Britney Spears, and Michael Jackson. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Bryan Adams and the second song is by Stevie Wonder? P(A and B)-

Answer 1

Answer:

Given that,

$\rightarrow$ Charles has 4 songs on a playlist each song is by a different artist. The artists are Bryan Adams, Stevie Wonder, Britney Spears and Michael Jackson.

$\rightarrow$ He programs his player to play the songs in a random order without repetition.

What is the probability that the first song is by Bryan Adams and the second song is by Stevie Wonder:

The probability of that first song is Bryan Adams is,

Since we have 4 singers and songs are shuffled at random with each having equal probability so total outcomes =4 and song of Bryan Adams is 1.

So the probability of that first song is by Bryan Adams=1/4.

Now Charles play song without repetition so there are 3 songs left in which 1 of Stevie Wonder so the probability of that second song is by Stevie Wonder= 1/3.

Hence the probability of that first song is by Bryan Adams and second song is by Stevie Wonder is,

P(A and B)=(1/4) $\times$ (1/3)

=1/12

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