Chapter 10.1, Problem 9E

a.

To determine

To calculate:

Probability of dice when sum is not $4$ .

Answer to Problem 9E

Probability of dice when sum is not $4$ is $\frac{8}{9}$ .

Explanation of Solution

Given information:

Two six sided dice are rolled there are $36$ possible outcomes.

Event: When sum is not $4$ .

Calculation:

The question is related to the number of possible outcomes.

The given experiment is rolling of two dices.

The event is two outcomes which comes up does not add up to $4$ ,

The required probability that two outcomes coming up will not add up to $4$ is,

  $P$ (Outcomes does not add to $4$ )

  $=1-P$ (Outcomes adds to $4$ )

  $\begin{array}{l}=1-\frac{4}{36}\\ =\frac{32}{36}\\ =\frac{8}{9}\end{array}$

Hence, the required probability of two numbers coming up which does not add up $4$ is $\frac{8}{9}$

b.

To determine

To calculate:

Probability of dice when sum is greater than $5$ .

Answer to Problem 9E

Probability of dice when sum is greater than $5$ is $\frac{25}{36}$ .

Explanation of Solution

Given information:

Two six sided dice are rolled there are $36$ possible outcomes.

Event: when sum is greater than $5$ .

The question is related to the number of possible outcomes.

The given experiment is rolling of two dices.

The event is two outcomes which comes up adds up to a number greater than is $5$ .

The required probability that two outcomes coming up will add up to number greater than is $5$ is,

  $P$ (Outcomes adds to number greater than $5$ )

  $=1-P$ (Outcomes adds to number less than $5$ .)

  $\begin{array}{l}=1-\frac{11}{36}\\ =\frac{25}{36}\end{array}$

Hence, the required probability of two numbers coming up which adds up to a number greater than $5$ is $\frac{25}{36}$ .