Chapter 7.2, Problem 7.27E

(a)

To determine

To Explain: the all possible outcomes in the sample space.

Explanation of Solution

Given:

Tossing a fair coin 4 times

Expected arrangement would be like that

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT

(b)

To determine

To Calculate: the probability would assign to each outcome.

Answer to Problem 7.27E

0.0625

Explanation of Solution

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

Each combinations are equally likely so

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{1}{16}\\ =0.0625\end{array}$

(c)

To determine

To Calculate: the probability for the getting three tails and one head.

Answer to Problem 7.27E

0.25

Explanation of Solution

Given:

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

Total sample space = 16

Favourable outcomes = 4

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{4}{16}\\ =0.25\end{array}$