Question

suppose you just purchased a digital music player and have put 9 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 9 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? (b) you like neither of them. (c) you like exactly one of them. (d) redo (a)-(c) if a song can be replayed before all 9 songs are played. (a) the probability that you like both songs is 0.157. (round to three decimal places as needed.) would it be unusual for you to like both of the songs? no yes

Explanation:

Step1: Calculate probability of liking first song

The probability of liking the first - song is the number of liked songs divided by the total number of songs. There are 4 liked songs out of 9 total songs, so $P(\text{like first song})=\frac{4}{9}$.

Step2: Calculate probability of liking second song given first is liked

After one liked song is played, there are 3 liked songs left out of 8 remaining songs. So $P(\text{like second song}|\text{like first song})=\frac{3}{8}$.

Step3: Calculate probability of liking both songs

By the multiplication rule of probability for dependent events $P(A\cap B)=P(A)\times P(B|A)$. So $P(\text{like both songs})=\frac{4}{9}\times\frac{3}{8}=\frac{12}{72}\approx0.167$.

Step4: Determine if it's unusual

An event is considered unusual if its probability is less than or equal to 0.05. Since $0.167>0.05$, it is not unusual.

Answer:

No