What is the probability of getting an even number when rolling a fair 6-sided die?
Answer: P(even) = 36 = 12 = 0.5.
Step-by-step solution
Given: A fair die: outcomes 1, 2, 3, 4, 5, 6, equally likely
To find: P(even number)
To find: P(even number)
Idea: List the sample space, pick out the favourable outcomes (the even numbers), and use P = favourablepossible.
- Sample space S = {1, 2, 3, 4, 5, 6}; number of possible outcomes = 6.½ mark
- Even numbers: {2, 4, 6}; number of favourable outcomes = 3.½ mark
- P(even) = 36 = 12 = 0.5 (50%).1 mark
P(getting an even number) = 3/6 = 1/2 = 0.5.
Check: Odd numbers {1, 3, 5} also give 36, and P(even) + P(odd) = 12 + 12 = 1 ✓.
Answer to write in the exam
S = {1, 2, 3, 4, 5, 6}; n(S) = 6
Even numbers = {2, 4, 6}; favourable outcomes = 3
∴ P(even) = 36 = 12
Common mistakes that cost marks
- Counting 0 as one of the outcomes. A die has no 0 face.
- Taking only 2 and 4 as even and forgetting 6, giving 26.
- Leaving the answer as 36 without simplifying to 12 (marks may be lost for an unsimplified fraction).
How this can come in the exam
MCQ (1 mark)
A fair die is rolled once. The probability of getting a prime number is
- 13
- 12
- 23
- 56
Show answer
(B) 12
Primes on a die: 2, 3, 5. P = 36 = 12.
Short answer (2 marks)
A fair die is rolled once. Find the probability of getting (a) a multiple of 3, (b) a number that is not a multiple of 3.
Show answer
(a) Multiples of 3: {3, 6}, so P = 26 = 13. (b) The other 4 numbers {1, 2, 4, 5}: P = 46 = 23. (Check: 13 + 23 = 1.)Try one yourself
A fair die is rolled once. What is the probability of getting an odd number greater than 1?
Show answer
Favourable {3, 5}: P = 26 = 13.
More questions like this
- Suppose you roll a 6-sided die 12 times and get a ‘3’ three times.
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- When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?
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