Chapter 6.2, Problem 1GP

Solution

To make: The probability distribution table for the given scenario and make the corresponding histogram.

$X$ (Sum)	2	3	4	5	6	7	8
Outcomes	1	2	3	4	3	2	1
$P\left(X\right)$	$\frac{1}{16}$	$\frac{1}{8}$	$\frac{3}{16}$	$\frac{1}{4}$	$\frac{3}{16}$	$\frac{1}{8}$	$\frac{1}{16}$

Given information:

Two 4 sided dice is thrown. Note the sum of the faces for the out come.

Formula used:

Probability of a certain event can be found by the following formula:

  $P\left(\text{Event}\right)=\frac{\text{Number}\text{of}\text{favorable}\text{outcome}}{\text{Number}\text{of}\text{total}\text{outcome}}$

Calculation:

Here, two dice are thrown each of which has 4 sides.

So, total number of outcomes will be $4^2=16$ .

\ The possible values of $X$ are the integers from 2 to 8. The table shows how many outcomes of rolling two dice produce each value of $X$ . Divide the number of outcomes for $X$ by 16 to find $P\left(X\right)$.

The probability distribution table is shown below:

$X$ (Sum)	2	3	4	5	6	7	8
Outcomes	1	2	3	4	3	2	1
$P\left(X\right)$	$\frac{1}{16}$	$\frac{1}{8}$	$\frac{3}{16}$	$\frac{1}{4}$	$\frac{3}{16}$	$\frac{1}{8}$	$\frac{1}{16}$

The histogram for the probability distribution corresponding to the random variable $X$ is shown below: