Chapter 12.6, Problem 10PPS

a.

To determine

To show that the probability distribution is valid

Answer to Problem 10PPS

The distribution of the probability is valid.

Explanation of Solution

Given information:

The probability distribution of bike is 17% or 0.17

The probability distribution of skateboards is 12% or 0.18

The probability distribution of inline skates is 24% or 0.24

The probability distribution of bike and skateboard is 12% or 0.12

The probability distribution of skate boards and inline skates is 15% or 0.15

The probability distribution of bikes and inline skates is 10 or 0.1

The probability distribution of all is 4% or 0.04

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 $\left(0.17+0.18+0.24+0.12+0.15+0.1+0.04\right)$ is equal to 1.

Therefore, the distribution of the probability is valid.

b.

To determine

To calculate:

The probability that a randomly chosen park allows bikes or skate boards

Answer to Problem 10PPS

The probability for randomly chosen park allows bike or skate board is $\frac{2}{3}$

Explanation of Solution

Given information:

The probability distribution of bike is 17% or 0.17

The probability distribution of skateboards is 12% or 0.18

The probability distribution of inline skates is 24% or 0.24

The probability distribution of bike and skateboard is 12% or 0.12

The probability distribution of skate boards and inline skates is 15% or 0.15

The probability distribution of bikes and inline skates is 10 or 0.1

The probability distribution of all is 4% or 0.04

Calculation:

Probability for a randomly chosen park allows bikes or skate boards can be calculated when its sum is formed,

Total number of equipment =3

Probability of only bike= $\frac{1}{3}$

Probability of only skate board = $\frac{1}{3}$

Probability of bike or skate board = $\frac{1}{3}+\frac{1}{3}$ = $\frac{2}{3}$

Therefore, the probability for a randomly chosen park allows bikes or skate boards is $\frac{2}{3}$

c.

To determine

To graph:

The probability distribution of skate parks

Explanation of Solution

Given information:

The probability distribution of bike is 17% or 0.17

The probability distribution of skateboards is 12% or 0.18

The probability distribution of inline skates is 24% or 0.24

The probability distribution of bike and skateboard is 12% or 0.12

The probability distribution of skate boards and inline skates is 15% or 0.15

The probability distribution of bikes and inline skates is 10 or 0.1

The probability distribution of all is 4% or 0.04

Graph:

  

Interpretation:

The graph for the probability distribution for skate parks can obtained by using the data from the probability distribution table. The given data is plotted in the bar graph