Chapter 14, Problem 1E

a)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 1E

Equally likely events.

Explanation of Solution

Given:

Toss 2 coins; record the order of heads and tails.

The events are said to be equally likely if it has an equal chance being selected.

The sample space for the given events is,

  $S=\{HH,HT,TH,TT\}$

Therefore, each outcome is equally likely, because you have an equal chance of tossing heads and tossing tails.

b)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 1E

Not equally likely events.

Explanation of Solution

Given:

A family has 3 children; record the number of boys.

The events are said to be equally likely if it has an equal chance being selected.

The sample space for the given events is,

  $S=\{0,1,2,3\}$

Therefore, it is more likely to have 2 boys than 3. Hence, events are not equally likely.

c)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 1E

Not equally likely events.

Explanation of Solution

Given:

Flip a coin until you get a head or 3 consecutive tails; record each flip.

The events are said to be equally likely if it has an equal chance being selected.

The sample space for the given events is,

  $S=\{H,TH,TTH,TTT\}$

Therefore, it is more likely to toss heads than it is to toss 3 consecutive tails. Hence, events are not equally likely.

d)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 1E

Not equally likely events.

Explanation of Solution

Given:

Roll two dice; record the large number.

The events are said to be equally likely if it has an equal chance being selected.

The sample space for the given events is,

  $S=\{H,TH,TTH,TTT\}$

Therefore, it only recording the larger number of 2 dice, 6 occur much more frequently than 1 or 2. Hence, events are not equally likely.