A fair 3-sided spinner is numbered 1, 2, 3. Write down the possible outcomes for one spin.
(1)
2
A bag contains one green, one orange and one pink counter. One counter is drawn at random. Write down the possible outcomes.
(1)
3
A fair coin is tossed once. How many possible outcomes are there?
(1)
4
A fair 5-sided spinner numbered 1 to 5 is spun once. How many possible outcomes are there?
(1)
5
Two fair coins are tossed. How many outcomes are in the sample space?
(1)
6
A fair six-sided die is rolled and a fair coin is tossed. How many outcomes are in the combined sample space?
(1)
7
A four-sided spinner has equal sections labelled W, X, Y, Z. The spinner is spun once, then a coin is tossed once. List the sample space of (spinner result, coin result) pairs.
(2)
8
A spinner has sections numbered 1 to 5. A fair coin is tossed and the spinner is spun. Write down the sample space of (coin, spinner) pairs and state how many outcomes there are.
(2)
9
A cafe lunch deal lets a customer choose one sandwich from ham or cheese, and one drink from juice, water or cola. List all the possible sandwich-and-drink combinations and state how many there are.
(2)
10
A bag contains two counters labelled P and Q only, one of each. A counter is picked at random, replaced, then a second counter is picked. List the sample space of ordered pairs.
(2)
11
A fair coin is tossed twice in a row. Draw up the sample space and use it to find the probability that at least one toss lands on heads.
(2)
12
Two fair 5-sided spinners, each numbered 1 to 5, are spun together. Use the sample space (25 outcomes) to find the probability that the sum of the two numbers shown is 6.
(2)
13
A fair six-sided die is rolled twice. Use the sample space to find the probability that the sum of the two rolls is 4.
(2)
14
A box contains three cards labelled 1, 2 and 3. A card is picked at random, replaced, then a second card is picked.
(a)List the sample space of ordered pairs.(1)
(b)Find the probability that the two cards picked show different numbers.(1)
15
Three fair coins are tossed. Find the probability of getting at least two heads. Use the sample space to help.
(3)
16
Two fair six-sided dice are rolled. Find the probability that the two dice show different numbers. Give your answer as a fraction in simplest form.
(3)
17
A fair coin is tossed and a fair 6-sided die is rolled. Find the probability that the coin shows heads or the die shows a 6 (or both).
(3)
18
A bag contains 4 counters labelled 1, 2, 3, 4. A counter is drawn at random, replaced, then a second counter is drawn. Find the probability that the sum of the two numbers drawn is greater than 6.
(3)
19
A spinner has 3 equal sections coloured red, white and blue. It is spun twice. Find the probability that at least one spin lands on red.
(3)
20
A fair 4-sided spinner numbered 1 to 4 is spun and a fair coin is tossed. Find the probability that the spinner shows an even number and the coin shows heads, or the spinner shows 1.
(3)
Mark scheme · KS3.M-P3D Listing Outcomes and Sample Space Diagrams: Fluency and Exam Drill
Question 1
B1 1, 2, 3 all listed cao
Answer: 1, 2, 3
Question 2
B1 green, orange, pink listed cao
Answer: green, orange, pink
Question 3
B1 2 cao
Answer: 2
Question 4
B1 5 cao
Answer: 5
Question 5
B1 4 cao
Answer: 4
Question 6
B1 12 cao
Answer: 12
Question 7
M1 method pairing each of the 4 letters with H and T
A1 complete list of 8: (W,H),(W,T),(X,H),(X,T),(Y,H),(Y,T),(Z,H),(Z,T) cao