Topics › KS3 › Probability
Relative frequency
-
A drawing pin is dropped 50 times. It lands point up 20 times. Estimate the probability that it lands point up.
A
Option A:
$\frac{20}{50}$
B
Option B:
$\frac{1}{2}$
C
Option C:
$\frac{20}{30}$
D
Option D:
$\frac{50}{20}$
Answer and misconceptions
A
Option A:
$\frac{20}{50}$
✓ Correct
B
Option B:
$\frac{1}{2}$
✗
Thinks two outcomes are equally likelyAssumes point up and point down each have a 50:50 chance, ignoring the results.
C
Option C:
$\frac{20}{30}$
✗
Compares successes with failuresWrites up : down (20 : 30) instead of up out of all 50 drops.
D
Option D:
$\frac{50}{20}$
✗
Divides the trials by the successesPuts the total on top, giving a value greater than 1.
-
A coin is flipped 10 times and lands on heads 7 times. Which statement is best?
A
Option A:
The coin must be biased
B
Option B:
The next flip is more likely to be tails
C
Option C:
More flips are needed to judge if it is fair
D
Option D:
The probability of heads is exactly 0.7
Answer and misconceptions
A
Option A:
The coin must be biased
✗
Thinks a small sample proves bias7 heads in 10 flips can easily happen with a fair coin.
B
Option B:
The next flip is more likely to be tails
✗
Thinks results even out (gambler's fallacy)The coin has no memory; past flips do not change the next one.
C
Option C:
More flips are needed to judge if it is fair
✓ Correct
D
Option D:
The probability of heads is exactly 0.7
✗
Treats relative frequency as the exact probabilityRelative frequency is only an estimate, and 10 trials is not many.
-
The probability a spinner lands on red is $0.2$. It is spun 50 times. How many times would you expect it to land on red?
A
Option A:
$0.2$
B
Option B:
$10$
C
Option C:
$250$
D
Option D:
$20$
Answer and misconceptions
A
Option A:
$0.2$
✗
Gives the probability, not the frequencyRepeats the probability instead of multiplying it by the 50 spins.
B
Option B:
$10$
✓ Correct
C
Option C:
$250$
✗
Divides by the probabilityWorks out 50 ÷ 0.2 instead of 50 × 0.2.
D
Option D:
$20$
✗
Reads 0.2 as 20 timesThinks a probability of 0.2 means 20 reds whatever the number of spins.
-
Four pupils each drop a cone and count how often it lands on its side. Whose results give the most reliable estimate of the probability?
A
Option A:
Ali: 9 times out of 10
B
Option B:
Ben: 1 time out of 2
C
Option C:
Cara: 150 times out of 200
D
Option D:
Dev: 140 times out of 400
Answer and misconceptions
A
Option A:
Ali: 9 times out of 10
✗
Picks the highest relative frequencyThinks a bigger fraction is more reliable; reliability depends on the number of trials.
B
Option B:
Ben: 1 time out of 2
✗
Picks the result closest to a halfThinks 50:50 looks fairest, but 2 trials tells us very little.
C
Option C:
Cara: 150 times out of 200
✗
Picks the most successes, not the most trialsCara has more successes (150) but Dev did more trials (400).
D
Option D:
Dev: 140 times out of 400
✓ Correct
-
After 40 spins, the relative frequency of blue is $0.3$. After 400 spins it is $0.26$. What is the best estimate of the probability of blue?
A
Option A:
$0.3$
B
Option B:
$0.28$
C
Option C:
$0.26$
D
Option D:
$0.56$
Answer and misconceptions
A
Option A:
$0.3$
✗
Trusts the first result mostUses the estimate from only 40 spins; the one from more trials is better.
B
Option B:
$0.28$
✗
Averages the estimates equallyGives both estimates equal weight, although one is based on 10 times as many spins.
C
Option C:
$0.26$
✓ Correct
D
Option D:
$0.56$
✗
Adds the relative frequenciesAdds 0.3 and 0.26; relative frequencies from repeated experiments are not added.