If you roll a standard 6-sided die, what is the theoretical probability of getting a 4?
Step-by-step solution
To find: P(rolling a 4)
Idea: For equally likely outcomes, P = Number of favourable outcomesNumber of possible outcomes. No experiment is needed.
- Number of favourable outcomes = 1 (only the number 4).½ mark
- Number of all possible outcomes = 6 (the numbers 1 through 6).½ mark
- P(rolling a 4) = 16 = 0.1666… ≈ 0.167 or 16.7%.1 mark
Check: Each of the 6 faces has probability 16, and 6 × 16 = 1, as the probabilities of all outcomes must add up to 1.
Answer to write in the exam
Number of favourable outcomes = 1 (the number 4)
Number of possible outcomes = 6
∴ P(rolling a 4) = 16 = 0.1666… ≈ 0.167 or 16.7%
Common mistakes that cost marks
- Writing 46 because the face is a 4. The favourable count is the number of faces showing 4, which is 1.
- Rounding 0.1666… to 0.166. To three decimal places it rounds up to 0.167.
- Mixing up theoretical and experimental probability: theoretical uses the count of equally likely outcomes, not results of rolls.
How this can come in the exam
A die is thrown once. The probability of getting a number less than 3 is
- 16
- 13
- 12
- 23
Show answer
(B) 13
Favourable outcomes {1, 2}: 2 of 6. P = 26 = 13.
Assertion (A): When a fair die is thrown, the probability of getting 6 is 16.
Reason (R): A die has 6 faces, and they are equally likely to come up.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
(A) Both A and R are true, and R is the correct explanation of A.
1 favourable face out of 6 equally likely faces gives 16; R is the reason.
Try one yourself
A fair die is rolled once. What is the theoretical probability of getting a 1? Write it as a fraction and a percentage.
Show answer
16 ≈ 0.167 ≈ 16.7%.
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