Question

Suppose you just purchased a digital music player and have put 13 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 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? ?(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 13 songs are played. ?(a) The probablility that you like both songs is nothing. ?(Round to three decimal places as? needed.) Would it be unusual for you to like both of the? songs? No Yes ?(b) The probability that you like neither song is nothing. ?(Round to three decimal places as? needed.) ?(c) The probability that you like exactly one song is nothing. ?(Round to three decimal places as? needed.) ?(d) The probability that you like both songs is nothing. ?(Round to three decimal places as? needed.) The probability that you like neither song is nothing. ?(Round to three decimal places as? needed.) The probability that you like exactly one song is nothing. ?(Round to three decimal places as? needed.)

Answer 1

(a)

(i)

like = 4

do not like = 9

Total songs = 13

P(First song: like) = 4/13 = 0.3077

like = 3

do not like = 9

Total songs = 12

P(Second song: like) = 3/12 = 0.25

So,

P(Like both of them) = 0.3077 X 0.25 = 0.0769

So,

Answer is:

0.077

This would not be unusual because Probability = 7.69 % > 5%

(b)

(i)

like = 4

do not like = 9

Total songs = 13

P(First song: do not like) = 9/13 = 0.6923

like = 4

do not like = 8

Total songs = 12

P(Second song: do not like) = 8/12 = 0.6667

So,

P(like neither of them) = 0.6923 X 0.6667 = 0.4615

So,

Answer is:

0.462

(c)

(i)

Case 1: First: like. AND Second: do not like:

like = 4

do not like = 9

Total songs = 13

P(First song: like) = 4/13 = 0.3077

like = 3

do not like = 9

Total songs = 12

P(Second song: do not like) = 9/12 = 0.75

So,

P(First: Like AND Second: do not like) = 0.3077 X 0.75 = 0.2308

Case 2: First: do not like. AND Second: like:

like = 4

do not like = 9

Total songs = 13

P(First song: do not like) = 9/13 = 0.6923

like = 4

do not like = 8

Total songs = 12

P(Second song: like) = 4/12 = 0.3333

So,

P(First: do not like AND Second: like) = 0.6923 X 0.3333 = 0.2308

So,

P(like exactly one of them) = 0.2308 + 0.2308 = 0.4615

Answer is:

0.462

(d)

(i)

like = 4

do not like = 9

Total songs = 13

P(First song: like) = 4/13 = 0.3077

like = 4

do not like = 9

Total songs = 13

P(Second song: like) = 4/13 = 0.3077

So,

P(Like both of them) = 0.3077² = 0.095

So,

Answer is:

0.095

(ii)

like = 4

do not like = 9

Total songs = 13

P(First song: do not like) = 9/13 = 0.6923

like = 4

do not like = 9

Total songs = 13

P(Second song: do not like) = 9/13 = 0.6923

So,

P(like neither of them) = 0.6923² = 0.479

So,

Answer is:

0.479

(iii)

Case 1: First: like. AND Second: do not like:

like = 4

do not like = 9

Total songs = 13

P(First song: like) = 4/13 = 0.3077

like = 4

do not like = 9

Total songs = 13

P(Second song: do not like) = 9/13 = 0.6923

So,

P(First: Like AND Second: do not like) = 0.3077 X 0.6923 = 0.2130

Case 2: First: do not like. AND Second: like:

like = 4

do not like = 9

Total songs = 13

P(First song: do not like) = 9/13 = 0.6923

like = 4

do not like = 9

Total songs = 13

P(Second song: like) = 4/13 = 0.3077

So,

P(First: do not like AND Second: like) = 0.6923 X 0.3077 = 0.2130

So,

P(like exactly one of them) = 0.2130 X 2 = 0.4260

Answer is:

0.426