A coin is tossed 25 times and lands on heads 14 times. Find the relative frequency of heads as a decimal.
(1)
2
A dice is rolled 40 times. The number 3 appears 5 times. Find the relative frequency of rolling a 3, giving your answer as a fraction in simplest form.
(1)
3
A spinner has 5 equal sections. It is spun 45 times. Find the expected frequency of landing on any one particular section.
(1)
4
A bag contains 3 green counters and 7 yellow counters. A counter is picked at random, its colour is noted, then it is replaced. This is repeated 60 times. Find the expected number of green picks.
(1)
5
A biased coin has probability 0.65 of landing on heads. It is tossed 20 times. Find the expected number of heads.
(1)
6
An event occurs 35 times out of 50 trials. Write down the relative frequency of the event as a percentage.
(1)
7
A spinner numbered 1 to 8 in equal sections is spun 32 times. Find the expected frequency of spinning a number greater than 6.
(1)
8
A coin is tossed 80 times and lands on heads 47 times. Calculate the relative frequency of heads as a decimal, and state whether the coin appears biased towards heads compared to a fair coin.
(2)
9
A dice is rolled 90 times. The number 2 appears 20 times. Calculate the relative frequency of rolling a 2, giving your answer as a fraction in simplest form.
(2)
10
A spinner with 6 equal sections is spun 150 times. Section D comes up 40 times. Find the expected frequency of section D, and state the difference between the experimental and expected frequencies.
(2)
11
A biased spinner has probability 0.2 of landing on red. It is spun 200 times. Find the expected number of red results, and the expected number of results that are not red.
(2)
12
A fair 10-sided spinner, numbered 1 to 10, is spun 500 times. Find the expected frequency of spinning a number that is a multiple of 5.
(2)
13
A quality-control test is carried out 250 times on a machine, and the machine fails 15 times. Calculate the relative frequency of failure as a decimal, giving your answer to 3 decimal places.
(2)
14
A charity raffle uses a spinner with 12 equal sections to select a jackpot section. In a trial of 300 spins, the jackpot section comes up 30 times. Calculate the relative frequency of landing on the jackpot section, state the theoretical probability of landing on the jackpot section, and say whether the spinner landed on the jackpot section more or less often than expected in this trial.
(3)
15
A school bus arrives late on 6 out of 40 days in a trial period. Use this data to estimate the probability that the bus is late on a randomly chosen day, and use your estimate to predict the number of late days out of the next 30 days.
(3)
16
A gardener plants sunflower seeds. In a trial, 34 out of 40 seeds germinate. Using this experiment as an estimate, find the probability that a seed fails to germinate, then predict how many seeds out of 500 would fail to germinate.
(3)
17
A factory tests bulbs from two production lines. Line A: 500 bulbs tested, 15 defective. Line B: 400 bulbs tested, 16 defective.
(a)Find the relative frequency of a defective bulb for Line A and for Line B.(2)
(b)State, with a reason, which line has the higher defect rate.(2)
18
A weather station records that it rained on 8 out of the past 25 days.
(a)Find the experimental probability of rain on a given day, giving your answer as a fraction in simplest form.(2)
(b)A forecaster claims the chance of rain in this season is 1/4. Compare the experimental probability to the forecaster's claim and state, with a reason, whether the data suggests the true chance is higher or lower than the claim.(2)
19
A theme park ride sometimes breaks down. Over a season, engineers recorded the ride running normally on 180 out of 200 opening days. Calculate the relative frequency that the ride runs normally on a given day, giving your answer as a decimal. Use this to estimate the number of days the ride would run normally over the next 400 opening days.
(4)
Mark scheme · KS3.M-P4D Experimental Probability and Relative Frequency: Fluency and Exam Drill
Question 1
B1 0.56 cao
Answer: 0.56
Question 2
B1 1/8 cao
Answer: 1/8
Question 3
B1 9 cao
Answer: 9
Question 4
B1 18 cao
Answer: 18
Question 5
B1 13 cao
Answer: 13
Question 6
B1 70% cao
Answer: 70%
Question 7
B1 8 cao
Answer: 8
Question 8
M1 relative frequency = 47/80 = 0.5875 shown
A1 0.5875 is greater than 0.5, so the coin appears slightly biased towards heads cao