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Suppose a compact disk​ (cd) you just purchased has 16tracks. after listening to the​ cd, you decide that you like 6of the songs. the random feature on your cd player will play each of the 16songs once in a random order. find the probability that among the first 5songs played​ (a) you like 2 of​ them; (b) you like 3 of​ them; (c) you like all 5of them.

Respuesta :

(a) you like 2 of them
(6/16) × (5/15) × (10/14) × (9/13) × (8/12) = 21,600/524,160
(out of 524,160 total possible combinations for the first 5 songs, 21,600 combinations play 2 of the 6 liked songs)
simplified, 21,600/ 524,160 = 135/3,276
(this is about a 4% chance)

(b) you like 3 of them
(6/16) × (5/15) × (4/14) × (10/13) × (9/12) = 10,800/524,160
(out of 524,160 total possible combinations for the first 5 songs, 10,800 combinations play 3 of the 6 liked songs)
simplified, 10,800/524,160 = 135/6,552
(this is about a 2% chance)

(c) you like all 5 of them
(6/16) × (5/15) × (4/14) × (3/13) × (2/12) = 720/524,160
(out of 524,160 total possible combinations for the first 5 songs, only 720 combinations play 5 of the 6 liked songs)
simplified, 720/524,160 = 9/6,552
(this is about a 0.1% chance)

The probability that among the first 5songs played​  

(a) Probability (you like [tex]2[/tex] of them) = 135/3276.

(b) Probability (you like [tex]3[/tex] of them) = 135/6552.

(c) Probability (you like all [tex]5[/tex] of them) = 9/6552.

What is probability?

The probability exists in the study of the possibilities of occurrence of a result, which are accepted by the proportion between favorable cases and possible cases.

(a) you like [tex]2[/tex] of them

Probability (you like [tex]2[/tex] of them)

[tex](6/16) *(5/15) * (10/14) *(9/13) * (8/12) = 21,600/524,160[/tex]

(out of [tex]524,160[/tex] total possible combinations for the first [tex]5[/tex] songs, [tex]21,600[/tex]combinations play [tex]2[/tex] of the [tex]6[/tex] liked songs)

[tex]21,600/ 524,160 = 135/3,276[/tex]

(this exists about a 4% chance)

(b) you like [tex]3[/tex] of them

Probability (you like [tex]3[/tex] of them)

[tex](6/16) *(5/15) * (4/14) * (10/13) * (9/12) = 10,800/524,160[/tex]

(out of [tex]524,160[/tex] total possible combinations for the first [tex]5[/tex] songs, [tex]10,800[/tex]combinations play [tex]3[/tex] of the [tex]6[/tex] liked songs)

[tex]10,800/524,160 = 135/6,552[/tex]

(this exists about a 2% chance)

(c) you like all [tex]5[/tex] of them

Probability (you like all [tex]5[/tex] of them)

[tex](6/16) * (5/15) * (4/14) * (3/13) * (2/12) = 720/524,160[/tex]

(out of [tex]524,160[/tex] total possible combinations for the first [tex]5[/tex] songs, only [tex]720[/tex]combinations play [tex]5[/tex] of the [tex]6[/tex] liked songs)

[tex]720/524,160 = 9/6,552[/tex]

(this exists about a 0.1% chance)

To learn more about probability

https://brainly.com/question/13604758

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