16 of 22 Save & Exit

Sample Space: Tutorial

Activity

In this exercise, you'll use the formula for the probability of the complement of an event.

Another game you've set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points

depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails).

Question 1

Find the total number of possible outcomes in each trial of this game.

The number of possible outcomes in each trial of this game is 12

Step-by-step explanation:

Given

Rolling of a 6 sided die followed by tossing of a fair coin

Required

Number of possible outcomes

The first step is to list out the possible outcomes of rolling a die and tossing a coin

Rolling a fair die = {1,2,3,4,5,6}

Tossing a coin = {Head, Tail}

Let Head be represented by H and Tail be represented by T;

So,

Rolling a fair die = {1,2,3,4,5,6}

Tossing a coin = {H, T}

The question states that a roll of a 6 sided die is followed by a toss of a fair coin

This means that each trial is {A roll of die and A toss of coin}

So, the sample space is as follows

Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}

Number of outcomes in the sample space is 12.

Hence, the number of possible outcomes in each trial of this game is 12