Probability - Worksheets, Questions and Revision

18 original exam-style questions - 14 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Probability

KS3.M-P1 Probability

AQA KS3.M-P1 · Calculator allowed · about 90 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
The probability scale below is used to describe how likely an event is.
0 0.5 1 impossible unlikely evens likely certain
(a)Write the probability of a certain event as a number.(1)
(b)Write the probability of an impossible event as a number.(1)
(c)An event is described as 'evens'. Write this probability as a fraction.(1)
(d)A weather app shows a 65% chance of rain tomorrow. Write this probability as a decimal.(1)
2
Choose the correct letter for each question below.
(a)Which of these cannot be a probability?(1)
  • A) 0
  • B) 0.5
  • C) 1
  • D) 1.2
(b)A probability of 3/4 is the same as which percentage?(1)
  • A) 34%
  • B) 43%
  • C) 75%
  • D) 25%
(c)Which of these events is impossible for a normal fair six-sided dice numbered 1 to 6?(1)
  • A) Rolling a 7
  • B) Rolling an even number
  • C) Rolling a 1
  • D) Rolling a number less than 6
3
A fair six-sided dice, numbered 1 to 6, is rolled once.
(a)Write down P(rolling a 3).(1)
(b)Find P(rolling an even number).(1)
(c)Find P(rolling a number greater than 4).(1)
(d)Find P(rolling a number less than 10).(1)
4
A bag contains 12 counters: 5 red, 4 blue and 3 green. One counter is picked at random.
(a)Find P(the counter is red).(1)
(b)Find P(the counter is not blue).(2)
(c)Amelia says, 'the probability of picking a green counter is 3.' Give a reason why Amelia is wrong.(1)
5
A survey asked 90 students at a school in Leeds to name their favourite sport from football, tennis or swimming. Some of the results are shown in the table below.
Football Tennis Swimming Total Boys Girls Total 25 10 50 8 12 40
(a)Complete the table, showing the number of boys who chose swimming, the number of girls who chose tennis, and the totals for each sport and the grand total.(3)
(b)A student is picked at random from all those surveyed. Find P(the student is a girl who chose tennis).(2)
(c)Find P(the student did not choose football).(2)
6
A biased spinner lands on one of four colours: red, blue, green or yellow only. P(red)=1/4, P(blue)=3/10, P(green)=1/5.
(a)Find P(the spinner lands on yellow).(2)
(b)The spinner is spun 60 times. Work out the expected number of times it lands on yellow.(2)
7
A spinner is divided into four sectors: red (90 degrees), blue (120 degrees), green (60 degrees) and yellow (90 degrees).
Red 90° Blue 120° Green 60° Yellow 90°
(a)Find P(the spinner lands on blue).(2)
(b)The spinner is spun 180 times. Work out the expected number of times it lands on green.(2)
(c)Find P(the spinner lands on red or yellow).(2)
8
Tom suspects a dice is biased. He rolls it 150 times. His results are shown in the table below.
Number 1 2 3 4 5 6 Total Frequency 20 18 22 19 41 30 150
(a)Estimate the probability that the dice lands on 5.(1)
(b)Give a reason to support Tom's suspicion that the dice is biased.(1)
(c)Using Tom's data, estimate how many times the dice would land on 5 in 500 rolls.(2)
9
A bag contains only red and blue counters. The probability of picking a red counter at random is 0.6. There are 40 counters in the bag.
(a)Find the number of red counters in the bag.(2)
(b)5 more blue counters are added to the bag (no red counters are added). Find the new probability of picking a red counter.(2)
10
A fair coin (Heads, Tails) is flipped and, at the same time, a fair spinner with three equal sections labelled 1, 2 and 3 is spun.
(a)List all the possible outcomes (the sample space) for the coin and the spinner together.(2)
(b)Find P(Tails and an odd number).(2)
(c)Find P(Heads or the number 2).(2)
11
A school raffle sells 500 tickets in total. Priya buys 20 tickets. One winning ticket is drawn at random.
(a)Find the probability that Priya wins the raffle.(2)
(b)The same raffle (500 tickets, with Priya always buying 20) is held once a week for 25 weeks of the school year, with all tickets replaced and re-sold each week. Work out how many times Priya would expect to win over the 25 weeks.(2)
(c)Give a reason why the number of times Priya actually wins over the 25 weeks might not equal your answer to part (b).(1)
12
Two fair six-sided dice are rolled together and the two scores are added.
Score on Dice B Score on Dice A + 1 2 3 4 5 6 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6 7 8 9 5 6 7 8 9 10 6 7 8 9 10 11 7 8 9 10 11 12 Total = Dice A score + Dice B score
(a)Find P(the total is 7).(2)
(b)Find P(the total is at least 10).(2)
(c)Find P(the total is a multiple of 5).(2)
13
A biased spinner lands on red, blue, green or yellow only. P(red)=0.15, P(blue)=0.35, P(green)=0.2.
(a)Find P(the spinner lands on yellow).(2)
(b)The spinner is spun 240 times. Work out the expected number of times it lands on blue.(2)
(c)Find P(the spinner lands on red or green).(1)
14
In a class of 30 students, 18 study French (F) and 14 study Spanish (S). 7 students study both languages.
Class of 30 students F S
(a)Draw a Venn diagram to show this information, and find the number of students who study French only.(2)
(b)Find the number of students who study neither language.(2)
(c)A student is picked at random from the class. Find P(the student studies Spanish only).(1)
(d)Find P(the student studies at least one of the two languages).(2)
15
A fair spinner has three equal sections coloured red, blue and green. It is spun twice.
Tree diagram: two spins of a 3-colour spinner 1st spin 2nd spin Outcome (probability) 1/3 1/3 1/3 Red Blue Green 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 Red Blue Green Red Blue Green Red Blue Green (R, R) 1/9 (R, B) 1/9 (R, G) 1/9 (B, R) 1/9 (B, B) 1/9 (B, G) 1/9 (G, R) 1/9 (G, B) 1/9 (G, G) 1/9 Each of the 9 outcomes has probability 1/3 x 1/3 = 1/9
(a)Draw a fully labelled tree diagram to show the possible outcomes and probabilities for the two spins.(2)
(b)Find P(both spins land on the same colour).(2)
(c)Find P(at least one of the two spins lands on red).(2)
16
A drawer contains 5 black socks and 3 white socks. Two socks are taken at random, one after the other, without replacement.
(a)Find P(both socks are black).(2)
(b)Find P(one sock of each colour is taken, in either order).(3)
(c)Find P(at least one white sock is taken).(2)
17
Ade drives through two sets of traffic lights on his route to work in Bristol. The two sets of lights act independently. The probability the first light is red is 0.4. The probability the second light is red is 0.25.
(a)Find P(both lights are red).(2)
(b)Find P(neither light is red).(2)
(c)Find P(exactly one of the two lights is red).(3)
(d)Show that P(both red) + P(neither red) + P(exactly one red) = 1.(1)
18
A biased coin has P(Heads) = 0.7. The coin is tossed three times.
(a)Find P(Heads all three times).(2)
(b)Find P(at least one Tail in the three tosses).(2)
(c)Find P(exactly two Heads and one Tail, in any order).(3)
Mark scheme · KS3.M-P1 Probability

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18