Question

A musical band has put out four albums, each of which has ten songs. A shuffled playlist is made where the band's forty songs appear in a random order.

What is the probability that the first and second songs in the playlist are both from the same album?

A. 0.5

B. 0.25

C. 0.0625

D. 0.0577

Answer 1

The probability that the first and second songs in the playlist are both from the same album is approximately 0.026.

Step-by-step explanation:

To find the probability that the first and second songs in the shuffled playlist are from the same album, we can consider the different possibilities. There are 4 albums, so there are 4 options for the first song. Once the first song is chosen, there are 10 songs remaining in that album, so there are 10 options for the second song. Therefore, the total number of favorable outcomes (songs from the same album) is 4*10 = 40. The total number of possible outcomes is 40*39 = 1560 (since there are 40 songs remaining for the second position after choosing the first song, and a total of 1560 different ways to choose two songs from the shuffled playlist). Therefore, the probability is 40/1560 = 0.025641026, which can be rounded to approximately 0.026.