Chapter 12.4, Problem 14PPS

a.

To determine

Create a frequency table and relative frequency graph of the data.

Answer to Problem 14PPS

  $\begin{array}{cccccccccccc}Outcome& BB& BG& BR& BW& GG& GR& GW& RR& RW& WW& Total\\ \mathrm{Re}lativefrequency& 0.047& 0.121& 0.161& 0.081& 0.061& 0.182& 0.091& 0.111& 0.121& 0.025& 1\end{array}$

  

Explanation of Solution

Given information:

Tai has a sack of $35$ marbles, $8black$ , $12$ red, $9$ green and rest are white. Brianna pulls $2$ marbles out of the bag.

Calculation:

Let use abbreviations for each color for example B for black ,

The possible sample space is,

  $S=\left[BB,BG.BR,BW,GG,GR,GW,RR,RW,WW\right]$

The number of ways to select $2$ marbles out of $35$ ,

  $C\left(35,2\right)=595$

The probability of selecting $2$ black marbles,

  $P\left(BB\right)=\frac{C\left(8,2\right)}{595}=0.047$

Similarly the frequency table will be,

  $\begin{array}{cccccccccccc}Outcome& BB& BG& BR& BW& GG& GR& GW& RR& RW& WW& Total\\ \mathrm{Re}lativefrequency& 0.047& 0.121& 0.161& 0.081& 0.061& 0.182& 0.091& 0.111& 0.121& 0.025& 1\end{array}$

The frequency graph will be,

  

b.

To determine

Find the most likely occurred outcome.

Answer to Problem 14PPS

The outcome one marble green and other red is most likely occurred.

Explanation of Solution

Given information:

Tai has a sack of $35$ marbles,

  $8black$ , $12$ red, $9$ green and rest are white. Brianna pulls $2$ marbles out of the bag.

Calculation:

The outcome one marble green and other red is most likely occurred.

c.

To determine

Find the $P\left(blackandgreen\right)$ .

Answer to Problem 14PPS

  $0.121$

Explanation of Solution

Given information:

Tai has a sack of $35$ marbles, $8black$ , $12$ red, $9$ green and rest are white. Brianna pulls $2$ marbles out of the bag.

Calculation:

The probability of green and black is,

  $P\left(blackandgreen\right)=0.121$