Chapter 12.6, Problem 12PPS

a.

To determine

To calculate:

The probability that a randomly chosen card is hockey or football

Answer to Problem 12PPS

The probability for a randomly chosen card is hockey or football is $34.28\%$

Explanation of Solution

Given information:

The number of baseball card is 53

The number of football card is 27

The number of basketball card is 39

The number of hockey card is 21

Calculation:

The probability for a randomly chosen card is hockey or football can be calculated as,

The sum of hockey and football card is divided by total number of cards

  $\begin{array}{l}\left(\frac{21+27}{53+27+39+21}\right)\times 100\%\\ =\left(\frac{48}{140}\right)\times 100\%\\ =0.3428\times 100\%\\ =34.28\%\end{array}$

Therefore, the probability for a randomly chosen card is hockey or football is $34.28\%$

b.

To determine

To calculate:

The probability distribution table for the given data and round it to nearest hundred

Answer to Problem 12PPS

The probability distribution table is,

baseball	0.38
football	0.19
basketball	0.28
hockey	0.15

Explanation of Solution

Given information:

The number of baseball card is 53

The number of football card is 27

The number of basketball card is 39

The number of hockey card is 21

Calculation:

The probability distribution table is made from the given data,

Baseball = $\left(\frac{53}{53+27+39+21}\right)=\left(\frac{53}{140}\right)=0.37$

Football = $\left(\frac{27}{53+27+39+21}\right)=\left(\frac{27}{140}\right)=0.19$

Basketball = $\left(\frac{39}{53+27+39+21}\right)=\left(\frac{39}{140}\right)=0.28$

Hockey = $\left(\frac{21}{53+27+39+21}\right)=\left(\frac{21}{140}\right)=0.15$

The probability distribution table is,

baseball	0.38
football	0.19
basketball	0.28
hockey	0.15

c.

To determine

To show that the probability distribution is valid

Answer to Problem 12PPS

The distribution of the probability is valid.

Explanation of Solution

Given information:

The number of baseball card is 53

The number of football card is 27

The number of basketball card is 39

The number of hockey card is 21

For probability distribution to be valid,

1. The probability of each value must be equal to or greater than zero or less than equal to 1
2. The addition of probabilities of value must be equal to 1

Here, every value is greater than zero and less than 1 and addition of values $\left(0.53+0.27+0.39+0.21\right)$ is equal to 1

Therefore,

The distribution of the probability is valid.

d.

To determine

To graph:

The probability distribution of Joshua’s sport card

Explanation of Solution

Given information:

The number of baseball card is 53

The number of football card is 27

The number of basketball card is 39

The number of hockey card is 21

Graph:

  

Interpretation:

The graph for the probability distribution of Joshua’s sport card can obtained by using the data from the probability distribution table. The given data is plotted in the bar graph