Topics › KS3 › Probability
Listing outcomes
-
A coin is flipped and a spinner numbered 1 to 4 is spun. How many different outcomes are there?
A
Option A:
6
B
Option B:
4
C
Option C:
8
D
Option D:
2
Answer and misconceptions
A
Option A:
6
✗
Adds the outcomes instead of multiplyingWorks out 2 + 4; each coin result can pair with every spinner number, so 2 × 4.
B
Option B:
4
✗
Counts only the spinner's outcomesLists 1, 2, 3, 4 but ignores that each can come with heads or tails.
C
Option C:
8
✓ Correct
D
Option D:
2
✗
Counts only the coin's outcomesLists heads and tails but ignores the spinner.
-
Two coins are flipped. Which list shows all the possible outcomes?
A
Option A:
HH, HT, TT
B
Option B:
HH, HT, TH, TT
C
Option C:
H, T
D
Option D:
HT, TH
Answer and misconceptions
A
Option A:
HH, HT, TT
✗
Treats HT and TH as the same outcomeHead then tail and tail then head are different outcomes for two different coins.
B
Option B:
HH, HT, TH, TT
✓ Correct
C
Option C:
H, T
✗
Lists outcomes for one coin onlyGives the outcomes of a single coin rather than combining both coins.
D
Option D:
HT, TH
✗
Leaves out outcomes where both coins matchForgets that both coins can land the same way (HH and TT).
-
Two ordinary dice are rolled and their scores are added. How many different totals are possible?
A
Option A:
36
B
Option B:
12
C
Option C:
6
D
Option D:
11
Answer and misconceptions
A
Option A:
36
✗
Counts all outcomes, not different totalsThere are 36 outcomes, but many give the same total; the totals go from 2 to 12.
B
Option B:
12
✗
Thinks the totals start at 1Counts 1 to 12, but the smallest total is 1 + 1 = 2.
C
Option C:
6
✗
Uses the outcomes of one dice onlyThinks the totals are the same as the scores on a single dice.
D
Option D:
11
✓ Correct
-
How many different 2-digit numbers can be made from the digits 1, 2 and 3, using each digit at most once in a number?
A
Option A:
6
B
Option B:
3
C
Option C:
9
D
Option D:
5
Answer and misconceptions
A
Option A:
6
✓ Correct
B
Option B:
3
✗
Thinks order does not matterCounts 12 and 21 as the same, but they are different numbers.
C
Option C:
9
✗
Allows a digit to be used twiceIncludes 11, 22 and 33, which repeat a digit.
D
Option D:
5
✗
Adds the choices instead of multiplyingThere are 3 choices for the first digit and 2 for the second, but works out 3 + 2.
-
Two fair dice are rolled and the scores are added. What is the probability of a total of 7?
A
Option A:
$\frac{1}{11}$
B
Option B:
$\frac{6}{36}$
C
Option C:
$\frac{3}{36}$
D
Option D:
$\frac{1}{36}$
Answer and misconceptions
A
Option A:
$\frac{1}{11}$
✗
Thinks every total is equally likelyUses the 11 possible totals as equally likely outcomes; there are 36 equally likely outcomes.
B
Option B:
$\frac{6}{36}$
✓ Correct
C
Option C:
$\frac{3}{36}$
✗
Counts 1 + 6 and 6 + 1 as one outcomeLists only 1+6, 2+5, 3+4, missing the reversed pairs on two different dice.
D
Option D:
$\frac{1}{36}$
✗
Thinks there is only one way to make 7Does not list the outcomes; there are six pairs that make 7.