The Mathematics of Maybe: Introduction to Probability | Exercise 7.3

Question 1

When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?

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Solution
Understand the Question
  • A standard 66-sided die has faces numbered 1,2,3,4,5,1, 2, 3, 4, 5, and 66.
  • The sample space SS is the set of all possible outcomes of an experiment.
  • The total number of outcomes is the number of elements in SS, denoted by n(S)n(S).

Step 1 · List the Sample Space

A standard 66-sided die has faces numbered from 11 to 66.Diagram 1

The set of all possible outcomes (sample space SS) is: S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}

Step 2 · Count the Number of Outcomes

The number of elements in the sample space is denoted as n(S)n(S):

n(S)=number of elements in S=6\begin{aligned} n(S) &= \text{number of elements in } S \\ &= 6 \end{aligned}
Answer

66

Common Mistakes
  • Including Zero: Assuming a die starts from 00; a standard die is numbered from 11 to 66.
  • Confusing Outcome with Probability: Stating the probability of an event (such as 16\dfrac{1}{6}) instead of the total count of outcomes in the sample space (66).

More questions in Exercise 7.3

Q1

When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?

Q2

For the following experiments write down the sample space SS.

(i) Rolling a die and tossing a coin together.

(ii) Choosing a random integer between −5-5 and +5+5.

(iii) A box containing 5 green and 7 red balls. One ball is drawn at random.

Q3

In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi.

(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.

(ii) List the event 'Selecting Samosa as a snack.'

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