Suppose you just purchased a digital music player and have put 12 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 12 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 12 songs are played.

a) 9%, not unusual

b) 42.4%

c) 48.4%

d) 11.1%, 44.4%, 44.4%

Step-by-step explanation:

We have the following information from the statement:

n = 12

r = 4

a)

P (likebothofthem) = P (likefirstsong) * P (likesecondsong)

P = 4/12 * 3/11

P = 0.09 = 9%

The probability is not unusual, unusual is considered less than 0.05 or 5%

b)

P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)

P = 8/12 * 7/11

P = 0.424 = 42.4%

c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)

P = (4/12 * 8/11) + (8/12 * 4/11)

P = 0.484 = 48.4%

d)

a)

P (likebothofthem) = P (likefirstsong) * P (likesecondsong)

P = 4/12 * 4/12

P = 0.111 = 11.1%

The probability is not unusual, unusual is considered less than 0.05 or 5%

b)

P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)

P = 8/12 * 8/12

P = 0.444 = 44.4%

c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)

P = (4/12 * 8/12) + (8/12 * 4/12)

P = 0.444 = 44.4%