Chapter 11.9, Problem 10E

a.

To determine

To state whether selection of first two songs played are independent or dependent

Answer to Problem 10E

The first two event are independent.

Explanation of Solution

Given information:

A CD player has two settings, random and shuffle. The shuffle setting plays all the songs on the CD only once in random order. The random setting selects songs randomly from the CD, but does not keep track of which songs have already been played.

The selection of both songs does not affect the outcomes of each other.

Hence the events are independent.

b.

To determine

To find the probability that song 3 is played first and then song 5 is played

Answer to Problem 10E

The probabilitythat the song 3 is played first and then song 5 is played is $\frac{1}{121}$ .

Explanation of Solution

Given information:

A CD player has two settings, random and shuffle. The shuffle setting plays all the songs on the CD only once in random order. The random setting selects songs randomly from the CD, but does not keep track of which songs have already been played.

Calculation:

Let P be the event that 3^rd song is played first and then song 5 is played.

Total numbers of songs is 11.

Therefore,

  $\begin{array}{l}P\text{ (3rd song is played first and then song 5 is played)}=\frac{1}{11}\times \frac{1}{11}\\ =\frac{1}{121}\end{array}$

Hence,

The probabilitythat the song 3 is played first and then song 5 is played is $\frac{1}{121}$ .

c.

To determine

To state whether selection of shuffled songs played are independent or dependent

Answer to Problem 10E

The event of selection of shuffled songs is dependent event.

Explanation of Solution

Given information:

A CD player has two settings, random and shuffle. The shuffle setting plays all the songs on the CD only once in random order. The random setting selects songs randomly from the CD, but does not keep track of which songs have already been played.

When songs are played in a shuffle manner, then the outcomes of each event may affect the outcomes of other events,

Hence the events are dependent.

d.

To determine

To find the probability that song 3 is played first and then song 5 is played when used in shuffled settings

Answer to Problem 10E

The probabilitythat song 3 is played first and then song 5 is played when used in shuffled settings is $\frac{1}{110}$ .

Explanation of Solution

Given information:

A CD player has two settings, random and shuffle. The shuffle setting plays all the songs on the CD only once in random order. The random setting selects songs randomly from the CD, but does not keep track of which songs have already been played.

Calculation:

Let P be the event that 3^rd song is played first and then song 5 is played.

Total numbers of songs is 11.

Therefore,

  $\begin{array}{l}P\text{ (3rd song is played first and then song 5 is played)}=\frac{1}{11}\times \frac{1}{10}\\ =\frac{1}{110}\end{array}$

Hence,

The probabilitythat song 3 is played first and then song 5 is played when used in shuffled settings is $\frac{1}{110}$ .