Chapter 13.8, Problem 15PPS

i.

To determine

To calculate: Probability by using tree diagram.

Answer to Problem 15PPS

Required probability for the given condition is $\frac{7}{16}$ .

Explanation of Solution

Given information:

Given condition is,

  $P$ (at least one $2$ )

Tree diagram for the given condition is,

A tree diagram gives the following possible outcomes:

  $\left\{2-1,2-2,2-3,2-4,5-1,5-2,5-3,5-4,6-1,6-2,6-3,6-4\right\}$

In order to keep the probabilities the same $6-1,6-2,6-3,6-4$ must be counted twice.

So there are $16$ possible outcomes. There are $7$ outcomes where there is at least one $2$ .

So, $P$ (at least one $2$ ) is $\frac{7}{16}$ .

Thus, the probability is $\frac{7}{16}$ .

ii.

To determine

To calculate: Probability by using tree diagram.

Answer to Problem 15PPS

Required probability for the given condition is $\frac{4}{16}$ or $\frac{1}{4}$ .

Explanation of Solution

Given information:

Given condition is,

  $P$ (at least one $3$ )

Tree diagram for the given condition is,

A tree diagram gives the following possible outcomes:

  $\left\{2-1,2-2,2-3,2-4,5-1,5-2,5-3,5-4,6-1,6-2,6-3,6-4\right\}$

According to the outcomes there are $4$ outcomes where there is at least one $3$ .

So, $P$ (at least one $3$ ) is $\frac{4}{16}$ or $\frac{1}{4}$ .

Thus, the probability is $\frac{4}{16}$ or $\frac{1}{4}$ .