Playing Music on Random Setting
Suppose that a Spotify p...

Question

Playing Music on Random Setting

Suppose that a Spotify playlist has 13 tracks. After listening to all the songs, you decide that you like 5 of them. With the random feature on the playlist, each of the 13 songs is played once in random order. Find the probability that among the first two songs played:

a. You like both of them. Would this be unusual?

Accepted Answer

A class has 20 students, of whom 6 earned an A on a test. 3 students are selected at random without replacement and called in order. What is the probability exactly 2 of the 1st 3 called earned in A? Is this outcome unusual at the 0.05 level? We have four possible answers, 0.02, 0.20, 0.01, or 0.30. We also want to check if the outcome is usual or not unusual. No. To solve this, we first need to find the total number of outcomes, which means the total number of ways of selecting 3 students from 20. This is given by a combination. N R equals in factorial, divided by R factorial, N minus R. Borial. Now, for the total case, our N is 20. R is 3. So we have 20 factorial, divided by 3 factorial, 20 minus 3 factorial. In the calculator, this is equal to 1140. Now from here, we need our favorable outcomes. Now, for our favorable, we're choosing 2 students from the 6 who earned an A. So we have 6, choose 2. This is multiplied. By the number of students, which is 1 student who did not earn an A from the 14 remaining. 14, choose one. This is given by 6 factorial divided by. 2 factorial, 6 minus 2 factorial, multiplied. By 14 factorial, 1 factorial, 14 minus 1 factorial. We can now simplify Putting these in the calculator gives us 15 multiplied by 14. Or 210. That means our probability then is our favorable outcomes. Divided by the total. 210 divided by 1140. Now, we can plug this into a calculator to get approximately 0.20 for our probability. Now, let's check if it's unusual or not. Now, is P less than 0.05. If so, it is unusual. However, we have 0.20, which is greater than 0.05. That means that this is not unusual. This means then the answer to our problem is answer B. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

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