Chapter 13.2, Problem 20PSC

(a)

To determine

To find: The number of pairs of numbers in the given figure.

Answer to Problem 20PSC

The number of pairs of numbers in the given figure are 16.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

As shown in the given figure there are total 16 dots, so there are total 16 pairs of numbers.

(b)

To determine

To find: The probability that $x=y$ .

Answer to Problem 20PSC

The probability that $x=y$ is $\frac{1}{4}$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

There are total 16 dots.

There are four possible cases $\left(0,0\right)$ , $\left(1,1\right)$ , $\left(2,2\right)$ , and $\left(3,3\right)$ which have $y=x$ .

Find the probability that $x=y$ is as follows.

  $\begin{array}{c}p=\frac{4}{16}\\ =\frac{1}{4}\end{array}$

Therefore, the probability that $x=y$ is $\frac{1}{4}$ .

(c)

To determine

To show: The points on the graph for which $x<y$ .

Answer to Problem 20PSC

The points on the graph for which $x<y$ are shown in figure (1).

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

The points on the graph for which $x<y$ are shown below.

  

Figure (1)

(d)

To determine

To find: The probability that $x<y$ .

Answer to Problem 20PSC

The probability that $x<y$ is $\frac{6}{16}$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

There are 6 dots out of 16 which has $x<y$ .

The probability that $x<y$ is as follows.

  $p=\frac{6}{16}$

Therefore, the probability that $x<y$ is $\frac{6}{16}$ .