Question

You look over the songs in a jukebox and determine that you like of the songs. ​(a) What is the probability that you like the next four songs that are​ played? (Assume a song cannot be​ repeated.) ​(b) What is the probability that you do not like the any of the next four songs that are​ played? (Assume a song cannot be​ repeated.) ​(a) The probability that you like the next four songs that are played is nothing. ​(Round to three decimal places as​ needed.) ​(b) The probability that you do not like any of the next four songs that are played is nothing. ​(Round to three decimal places as​ needed.)

Answer 1

Complete Question

You look over the songs in a jukebox and determine that you like 18 of 59 songs.

(a) What is the probability that you like the next four songs that are played? (Assume a song cannot be repeated) Round to three decimal places as needed)

(b) What is the probability that you do not like the next four songs that are played? (Assume a song cannot be repeated.) Round to three decimal places as needed

Answer:

a

`P = 0.0067`

b

`Q = 0.222`

Explanation:

From the question we are told that

The total number of songs is
`n = 59`

The number of songs you liked is
`k = 18`

The probability that you like the next four songs that are played? (Assume a song cannot be repeated) is mathematically represented as

`P = ( ^(k) C _4 )/( ^(n) C _4)`

=>
`P = ( ^(18) C _4 )/( ^(59) C _4)`

Now using a combination calculator

`P= ( 3060)/( 455126)`

`P = 0.0067`

The probability that you do not like the next four songs that are played? (Assume a song cannot be repeated.) is mathematically evaluated as

`Q = ( ^(n- k) C _4 )/( ^(n) C _4)`

=>
`Q = ( ^(59- 18) C _4 )/( ^(n) C _4)`

=>
`Q = ( ^(41) C _4 )/( ^(59) C _4)`

Now using a combination calculator

`Q = ( 101270)/( 455126)`

`Q = 0.222`