The probability scale below shows five points, labelled P, Q, R, S and T, marked at equal intervals between 0 and 1.
(a)Sam rolls an ordinary fair dice numbered 1 to 6. Write down the letter of the point that best represents the probability that the score is less than 7.(1)
(b)A card is picked at random from a standard, well-shuffled pack of 52 playing cards. Write down the letter of the point that best represents the probability that the card is a spade.(1)
(c)A fair coin is flipped once. Write down the letter of the point that best represents the probability that it lands on tails.(1)
(Total for Question 1 is 3 marks)
2
A fair spinner is equally likely to land on each of the numbers 1, 2, 3, 4 and 5. Write down the probability that it lands on an odd number.
(Total for Question 2 is 1 mark)
3
The probability that a particular bus arrives on time is 0.71. Write down the probability that the bus does not arrive on time.
(Total for Question 3 is 1 mark)
4
Chloe has a bag containing only 6 lime sweets, 5 blackcurrant sweets and 9 orange sweets. She takes one sweet from the bag at random. Work out the probability that the sweet is lime or blackcurrant. Give your answer as a fraction in its simplest form.
(Total for Question 4 is 2 marks)
5
A fair spinner can land on amber, teal or violet. The table shows two of the probabilities.
Colour
Amber
Teal
Violet
Probability
0.28
y
0.39
Work out the value of y.
(Total for Question 5 is 2 marks)
6
Jakub spins a spinner 80 times. It lands on green 24 times.
(a)Calculate the relative frequency of green.(1)
(b)Jakub is going to spin the spinner a further 220 times. Estimate how many more times it will land on green.(2)
(Total for Question 6 is 3 marks)
7
Spinner X can land on red or green. Spinner Y can land on 1, 2 or 3. Both spinners are spun once. List all the possible outcomes.
(Total for Question 7 is 2 marks)
8
A fair coin is flipped once and, at the same time, a fair four-sided spinner numbered 1 to 4 is spun once. Find the probability of getting a head and a number greater than 2.
(Total for Question 8 is 2 marks)
9
At Freya's market stall, every customer chooses tea, coffee or water. These are the only three drinks available and each customer chooses exactly one. P(tea) = 0.34 and P(coffee) = 0.41.
(a)Work out P(water).(2)
(b)Work out P(tea or water).(1)
(Total for Question 9 is 3 marks)
10
100 students in Year 10 were asked whether they walk or take the bus to school. The incomplete two-way table shows some of the results.
(a)Complete the two-way table.(2)
(b)One student is picked at random from all 100 students. Find the probability that the student is a boy who takes the bus.(2)
(c)Given that the student picked walks to school, find the probability that the student is a girl.(2)
(Total for Question 10 is 6 marks)
11
The Venn diagram shows information about 60 members of a drama club. S = members who can sing. D = members who can dance. Only sing = 18, only dance = 12, both sing and dance = 15, neither = 15.
(a)Write down n(S ∩ D).(1)
(b)Write down the number of members who can dance.(1)
(c)A member is picked at random. Find P(S ∪ D)'.(2)
(d)Write down P(D ∩ S').(2)
(Total for Question 11 is 6 marks)
12
A biased spinner has P(lands on blue) = 0.3. The spinner is spun twice. Find the probability that it lands on blue both times.
(Total for Question 12 is 2 marks)
13
A fair spinner is numbered 1 to 8. It is spun 96 times. Work out an estimate for the number of times it lands on a number greater than 5.
(Total for Question 13 is 2 marks)
14
P(Idris wins a prize in the tombola) = 2/9. Write down the probability that Idris does not win a prize.
(Total for Question 14 is 1 mark)
15
A fair four-sided dice, with faces numbered 1 to 4, is rolled twice. The two scores are multiplied together. Find the probability that the product is 4.
(Total for Question 15 is 2 marks)
16
A fair dice is numbered 1 to 20. It is rolled once. Find the probability that the number is a multiple of 5 or a multiple of 8.
(Total for Question 16 is 2 marks)
17
Meera has a biased spinner with P(lands on red) = 0.65 and P(lands on blue) = 0.35. She spins the spinner twice.
(a)Complete the tree diagram to show the probabilities for both spins.(2)
(b)Work out the probability that the spinner lands on the same colour both times.(3)
(Total for Question 17 is 5 marks)
18
A box contains 9 chocolates: 4 dark and 5 milk. Ben takes a chocolate at random from the box and eats it. He then takes a second chocolate at random from the box and eats it.
(a)Complete the tree diagram to show the probabilities for both chocolates.(3)
(b)Work out the probability that both chocolates are dark.(2)
(c)Work out the probability that exactly one of the two chocolates is dark.(3)
(Total for Question 18 is 8 marks)
19
A holiday company surveyed 120 travellers. 70 of the travellers were adults and the rest were children. 45 of the adults travelled by plane and the rest of the adults travelled by coach. Of the children, 28 travelled by coach and the rest travelled by plane.
(a)Use this information to draw and complete a two-way table showing adults and children against plane and coach.(4)
(b)One traveller is picked at random from all 120 travellers. Find the probability that the traveller is a child who travelled by plane.(2)
(Total for Question 19 is 6 marks)
20
In a survey of 100 office workers, some cycle to work (C) and some drive to work (D). The number who only cycle is 2x, the number who both cycle and drive is x, the number who only drive is 3x, and the number who do neither is 16.
(a)Form and solve an equation to find the value of x.(3)
(b)A worker is picked at random. Find the probability that the worker cycles to work (whether or not they also drive).(3)
(Total for Question 20 is 6 marks)
21
Events A and B are such that P(A) = 0.4, P(B) = 0.45 and P(A ∩ B) = 0.18. Determine, showing full working, whether events A and B are independent.
(Total for Question 21 is 3 marks)
22
A bag contains 20 counters that are only red or yellow. Two red counters are removed from the bag and not replaced. There are now twice as many yellow counters as red counters left in the bag. Work out how many red counters were in the bag originally.
(Total for Question 22 is 4 marks)
23
A fair five-sided spinner is numbered 1, 2, 3, 4, 5. It is spun twice and the two scores are added together. Sara says, 'The probability of getting a total of 6 is the same as the probability of getting a total of 10.' Determine whether Sara is correct. You must show your working.
(Total for Question 23 is 4 marks)
24
A drawer contains n socks. Exactly 4 of the socks are grey and the rest are black. Priti takes two socks at random from the drawer, without replacement. The probability that she takes two grey socks is 1/6.
(a)Show that n2 - n - 72 = 0.(3)
(b)Solve the equation to find the value of n.(3)
(Total for Question 24 is 6 marks)
25
The probability that a biased coin lands on heads is p. The coin is flipped twice. The probability of getting two heads is 1/2 more than the probability of getting two tails.
(a)Form an equation in p, and simplify it using the difference of two squares.(2)
(b)Solve your equation to find the value of p.(2)
(Total for Question 25 is 4 marks)
Mark scheme · 4.19D Probability: Fluency and Exam Drill
Question 1
(a) B1 T cao
(a) Answer: T
(b) B1 Q cao
(b) Answer: Q
(c) B1 R cao
(c) Answer: R
Question 2
B1 3/5 oe (accept 0.6, 60%)
Answer: 3/5
Question 3
B1 0.29 oe
Answer: 0.29
Question 4
M1 (6+5)/20 oe
A1 11/20 cao
Answer: 11/20
Question 5
M1 1 - 0.28 - 0.39 oe
A1 y = 0.33 cao
Answer: y = 0.33
Question 6
(a) B1 0.3 oe (accept 3/10, 30%)
(a) Answer: 0.3
(b) M1 0.3 x 220 oe, ft their (a)
(b) A1 66 cao
(b) Answer: 66
Question 7
M1 at least 4 correct outcomes shown
A1 all 6 outcomes listed with no repeats: (red,1), (red,2), (red,3), (green,1), (green,2), (green,3)