Chapter 13.CT, Problem 1CT

Describe each event as a set of outcomes.

a. When two dice are rolled, we obtain a total greater than nine.

b. When four coins are flipped, we get more heads than tails.

To determine

a)

To Describe:

The event as a set of outcomes.

Answer to Problem 1CT

Solution:

The set of outcomes for the event $A\text{ is }\left\{\begin{array}{llllll}\left(4,6\right),\hfill & \left(5,5\right),\hfill & \left(5,6\right),\hfill & \left(6,\text{ 4}\right),\hfill & \left(6,5\right),\hfill & \left(6,6\right)\hfill \end{array}\right\}.$

Explanation of Solution

Given,

Roll two dice, the total greater than nine.

The sample space for this experiment consists of the following 36 pairs.

$\left\{\begin{array}{llllll}\left(1,1\right),\hfill & \left(1,2\right),\hfill & \left(1,\text{ 3}\right),\hfill & \left(1,4\right),\hfill & \left(1,5\right),\hfill & \left(1,6\right),\hfill \\ \left(2,1\right),\hfill & \left(2,2\right),\hfill & \left(2,3\right),\hfill & \left(2,4\right),\hfill & \left(2,5\right),\hfill & \left(2,6\right),\hfill \\ \left(3,1\right),\hfill & \left(3,2\right),\hfill & \left(3,3\right),\hfill & \left(3,4\right),\hfill & \left(3,\text{ 5}\right),\hfill & \left(3,6\right),\hfill \\ \left(4,1\right),\hfill & \left(4,2\right),\hfill & \left(4,3\right),\hfill & \left(4,4\right),\hfill & \left(4,5\right),\hfill & \left(4,6\right),\hfill \\ \left(5,1\right),\hfill & \left(5,2\right),\hfill & \left(5,3\right),\hfill & \left(5,4\right),\hfill & \left(5,5\right),\hfill & \left(5,6\right),\hfill \\ \left(6,1\right),\hfill & \left(6,2\right),\hfill & \left(6,3\right),\hfill & \left(6,4\right),\hfill & \left(6,5\right),\hfill & \left(6,6\right),\hfill \end{array}\right\}$

Let A be a event of getting a total greater than nine.

Set of outcomes for event $A\text{ = }\left\{\begin{array}{llllll}\left(4,6\right),\hfill & \left(5,5\right),\hfill & \left(5,6\right),\hfill & \left(6,\text{ 4}\right),\hfill & \left(6,5\right),\hfill & \left(6,6\right)\hfill \end{array}\right\}.$

Hence, the set of outcomes for the event $A\text{ is }\left\{\begin{array}{llllll}\left(4,6\right),\hfill & \left(5,5\right),\hfill & \left(5,6\right),\hfill & \left(6,\text{ 4}\right),\hfill & \left(6,5\right),\hfill & \left(6,6\right)\hfill \end{array}\right\}.$

To determine

b)

To Describe:

The event as a set of outcomes.

Answer to Problem 1CT

Solution:

The set of outcomes,

$A=\left\{\text{HHHT, HHTH, HTHH, THHH, HHHH}\right\}$

Explanation of Solution

Given,

Flipping four coins.

The sample space for flipping four coins is given by,

$S=\left\{\begin{array}{ll}\text{HHHH}\hfill & \text{THHH}\hfill \\ \text{HHHT}\hfill & \text{THHT}\hfill \\ \text{HHTH}\hfill & \text{THTH}\hfill \\ \text{HHTT}\hfill & \text{THTT}\hfill \\ \text{HTHH}\hfill & \text{TTHH}\hfill \\ \text{HTHT}\hfill & \text{TTHT}\hfill \\ \text{HTTH}\hfill & \text{TTTH}\hfill \\ \text{HTTT}\hfill & \text{TTTT}\hfill \end{array}\right\}$

Let A be the event of getting more heads than tails.

Set of outcomes for event,

$A=\left\{\text{HHHT, HHTH, HTHH, THHH, HHHH}\right\}$

Hence, the set of outcomes,

$A=\left\{\text{HHHT, HHTH, HTHH, THHH, HHHH}\right\}$