Probability · Ages 14–15
Listing outcomes in a table
Two dice: 36 cells; count the favourable ones. The sums aren't equally likely.
How to do it
Method
Two dice: 36 cells; count the favourable ones. The sums aren't equally likely
Sum 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), P = 536
Another way
The diagonals
Sum 8: 13 − 8 = 5 cells
In full
When two things happen together (two dice, a coin and a die, two spinners), list the sample space in a table: one thing's outcomes down the left, the other's across the top, and each cell one outcome. Two dice give 6 × 6 = 36 cells, all equally likely. A sum of 8 comes from (2, 6), (3, 5), (4, 4), (5, 3), (6, 2): 5 cells, probability 536. Careful: the sums 2 to 12 are 11 values, but not equally likely, so it isn't 111. Another way: where there's a pattern, count it straight. Cells with sum s lie on a diagonal: for s from 2 to 7 there are s − 1 of them, for s from 7 to 12 there are 13 − s, so a sum of 8 has 13 − 8 = 5. For "at least" events, take the opposite from 1: at least one 6 on two dice is the opposite of no 6 at all, 5 × 5 = 25 cells, so P = 1 − 2536 = 1136.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Chi-keung rolls two dice. The table lists the sum of the two. The probability of a sum of 6 is .
Answer in simplest form
Show the answer and working
Answer: 536
The 36 cells are equally likely, and 5 show 6: 536 = 536.
Example 2
Ka-yee tosses a coin and rolls a die together. The probability of tails with a number greater than 3 is .
Answer in simplest form
Show the answer and working
Answer: 14
In a table, 2 coin outcomes × 6 die outcomes = 12 cells; tails with more than 3 fills 3 of them: 312 = 14.
Example 3
Two dice are rolled. Which sum is the most likely?
- A. 5
- B. 4
- C. 12
- D. 7
Choose the right answer
Show the answer and working
Answer: D. 7
A sum of 7 comes from (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1): 6 cells, the table's longest diagonal.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Two dice are rolled. The table lists the product of the two. The probability of a product greater than 13 is .
Answer in simplest form
Answer:
2.Ming rolls two dice. The table lists the sum of the two. The probability of a sum of 10 is .
Answer in simplest form
Answer:
3.Ka-yan tosses a coin and rolls a die together. The probability of tails with a number greater than 0 is .
Answer in simplest form
Answer:
4.Tsz-hin rolls two dice, and the table lists the difference (larger minus smaller). The sample space has outcomes; of them have a difference of 1.
Fill in each blank
Answer:
5.Rolling two dice, a sum of 8 is exactly as likely as a sum of 6.
True or false?
Answer:
All the answers
- 1. 1336
- 2. 112
- 3. 12
- 4. 36, 10
- 5. True
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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