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4.19F Probability: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A spinner has four equal sections coloured red, blue, green and yellow. What is the probability that one spin lands on green?

(Total for Question 1 is 1 mark)

A fair six-sided die is rolled once. What is the probability of rolling an odd number?

(Total for Question 2 is 1 mark)

A bag contains 5 red counters and 3 blue counters. A counter is taken at random. Work out the probability the counter is blue.

(Total for Question 3 is 2 marks)

A bag contains 2 white, 4 black and 4 green counters. A counter is chosen at random. Work out the probability the counter is not black.

(Total for Question 4 is 2 marks)

A coin is flipped twice. List all possible outcomes using H for heads and T for tails, and then write down the probability of getting exactly one head.

(a)List all possible outcomes.(1)

(b)Work out the probability of exactly one head.(2)

(Total for Question 5 is 3 marks)

A jar contains 3 strawberry sweets, 2 mint sweets and 5 lemon sweets. One sweet is taken at random. Work out the probability the sweet is strawberry or lemon.

(Total for Question 6 is 4 marks)

A bag contains counters labelled 1, 2, 3 and 4. A counter is chosen at random and then replaced. Two independent draws are made. Work out the probability that the first draw is 3 and the second draw is less than 3.

(Total for Question 7 is 4 marks)

A fair spinner has three equal regions labelled A, B and C. Jamie spins the spinner twice. Work out the probability Jamie gets A both times.

(a)Work out the probability of getting A on one spin.(1)

(b)Work out the probability Jamie gets A on both spins. Show your method.(4)

(Total for Question 8 is 5 marks)

Two coins are different: one is a 1 pence coin and one is a 2 pence coin. Both are fair. They are flipped once. Find the probability that the total value of coins that land heads is 3 pence.

(Total for Question 9 is 3 marks)

A bag contains 6 red counters and 4 blue counters. Two counters are drawn at random without replacement. Work out the probability that both counters are red.

(Total for Question 10 is 5 marks)

A spinner is divided into three unequal regions. The probabilities of landing on X, Y and Z are 1/6, 1/3 and 1/2 respectively. The spinner is spun twice. Work out the probability that at least one spin lands on Z.

(Total for Question 11 is 5 marks)

A bag contains 4 green, 3 purple and 3 orange counters. Two counters are drawn at random without replacement. Work out the probability that the two counters are different colours.

(Total for Question 12 is 5 marks)

Mark scheme · 4.19F Probability: Foundation Tier Practice

Question 1

B1 1/4 cao
Answer: 1/4 (or 0.25 or 25%)

Question 2

B1 3/6 or 1/2 cao
Answer: 1/2 (or 0.5 or 50%)

Question 3

M1 correct fraction method 3/(5+3) oe
A1 3/8 cao
Answer: 3/8

Question 4

M1 1 - P(black) or (2+4)/10 shown oe
A1 6/10 = 3/5 cao
Answer: 3/5

Question 5

(a) B1 list: HH, HT, TH, TT (in any order) oe
(a) Answer: HH, HT, TH, TT
(b) M1 2 favourable outcomes (HT, TH) shown out of 4
(b) A1 1/2 cao
(b) Answer: 1/2

Question 6

M1 identify favourable outcomes 3+5 and total 3+2+5 = 10
M1 state the fraction 8/10 oe
M1 show method to simplify 8/10 to 4/5
A1 4/5 cao
Answer: 4/5

Question 7

M1 P(first = 3) = 1/4 identified
M1 P(second < 3) = 2/4 identified
M1 multiply probabilities for independent events: (1/4) x (2/4) = 2/16 shown
A1 1/8 cao
Answer: 1/8

Question 8

(a) B1 1/3 cao
(a) Answer: 1/3
(b) M1 state independence and multiply: (1/3) x (1/3) oe
(b) M1 multiply to give 1/9
(b) M1 show product as fraction 1/9 oe
(b) A1 1/9 cao
(b) Answer: 1/9

Question 9

M1 list of all four equally likely outcomes for heads/tails on the two coins, e.g. (1p H,2p H), (1p H,2p T), (1p T,2p H), (1p T,2p T) or equivalent
M1 identify favourable outcome(s): both coins heads gives total 3p
A1 1/4 cao
Answer: 1/4

Question 10

M1 P(first red) = 6/10 stated
M1 P(second red after first red) = 5/9 stated
M1 multiply probabilities: (6/10) x (5/9) shown
M1 simplify product 30/90 shown
A1 1/3 cao
Answer: 1/3

Question 11

M1 identify P(Z) = 1/2
M1 calculate P(no Z in one spin) = 1 - 1/2 = 1/2 or state directly 1/2
M1 compute P(no Z in two spins) = (1/2) x (1/2) = 1/4
M1 use complement: 1 - 1/4 shown
A1 3/4 cao
Answer: 3/4

Question 12

M1 calculate total outcomes denominator 10 x 9, or work with probabilities sequentially
M1 calculate probability both same colour: P(both green) = (4/10)*(3/9) and P(both purple) = (3/10)*(2/9) and P(both orange) = (3/10)*(2/9) or equivalent
M1 sum same-colour probabilities: (4/10)*(3/9) + (3/10)*(2/9) + (3/10)*(2/9) = (12 + 6 + 6)/90 = 24/90 shown
M1 use complement: 1 - 24/90 = 66/90 shown
A1 simplify to 11/15 cao
Answer: 11/15

Probability: Foundation Tier Practice - Worksheets, Questions and Revision