When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?
Answer: S = {1, 2, 3, 4, 5, 6}, so n(S) = 6.
Step-by-step solution
Idea: List every face that can come up, once each, and count them. The count is the sample size n(S).
- The faces of the die show 1, 2, 3, 4, 5 and 6, so S = {1, 2, 3, 4, 5, 6}.½ mark
- Total number of possible outcomes n(S) = 6.½ mark
There are 6 possible outcomes: S = {1, 2, 3, 4, 5, 6}, n(S) = 6.
Answer to write in the exam
S = {1, 2, 3, 4, 5, 6}
∴ Total number of possible outcomes n(S) = 6
Common mistakes that cost marks
- Answering 1 (“one die, one outcome”). The question asks how many results are possible, not how many come up in one roll.
- Including 0 in the sample space. A die has no 0 face.
- Answering 36. That is the number of outcomes for rolling two dice.
How this can come in the exam
MCQ (1 mark)
A spinner is divided into 10 equal sectors numbered 1 to 10. The number of elements in the sample space for one spin is
- 1
- 5
- 10
- 20
Show answer
(C) 10
S = {1, 2, …, 10}, so n(S) = 10.
MCQ (1 mark)
A letter is picked from the English alphabet. The sample size n(S) is
- 5
- 21
- 24
- 26
Show answer
(D) 26
There are 26 letters, A to Z.
Try one yourself
A card is drawn from 12 cards numbered 1 to 12. What is the total number of possible outcomes?
Show answer
12 (S = {1, 2, …, 12}).
More questions like this
- For the following experiments write down the sample space S.
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- There are two fruit baskets A and B. Basket A has one apple and two oranges. Basket B has one banana and one mango. You randomly pick one fruit from each basket.