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

  $Q = 0.222$

Step-by-step 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

        $P = \frac{ ^{k} C _4 }{ ^{n} C _4}$

=>     $P = \frac{ ^{18} C _4 }{ ^{59} C _4}$

Now using a combination calculator

       $P= \frac{ 3060}{ 455126}$

       $P = 0.0067$

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

     $Q = \frac{ ^{n- k} C _4 }{ ^{n} C _4}$

=>  $Q = \frac{ ^{59- 18} C _4 }{ ^{n} C _4}$

=>  $Q = \frac{ ^{41} C _4 }{ ^{59} C _4}$

Now using a combination calculator

      $Q = \frac{ 101270}{ 455126}$

      $Q = 0.222$