Question

George Martin loves The Beatles. Honestly, who doesn’t? On George’s favorite Spotify playlist, 40% of the songs are by The Beatles. During a long road trip, George shuffled his playlist and listened to 30 songs. What is the probability that at least half of the songs on the trip were by The Beatles? Don’t forget to check appropriate conditions before you do your computations. Note: you can assume the playlist is infinite in length.

Answer 1

Answer:

17.5%

Step-by-step explanation:

First of all, see this situation as a cumulative binomial distribution. You have isolated trials with a probability of success. This makes it binomial. The wording of the question "what is the probability of at least half..." makes this cumulative.

There are a few ways to calculate this, and I'm not quite sure which way you're familiar with. I'll show the cumbersome way and use wolfram to make the calculation.

First, I'll calculate the probability for 15 success, given 30 trials.

30c15*0.4^15*0.6^15

Since the question asks for the probability of at least 15 success, I'll have to make a calculation for the probability of 16 successes, then 17, and so on. Then I'll have to add all the probabilities together. So, I'll use wolfram for that (see attached)