Probability (Foundation) (Part 2) - Worksheets, Questions and Revision

18 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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FOUNDATION

2.12B Probability (Foundation) (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 85 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A box contains 12 balls. All of the balls are yellow. A ball is taken from the box at random.

(a)Write down the probability that the ball is yellow.(1)

(b)Write down the probability that the ball is green.(1)

(Total for Question 1 is 2 marks)

This question is about probability.

Figure (to be drawn): A blank probability scale, drawn as a straight line with 0 marked at the left-hand end and 1 marked at the right-hand end, with no other markings.

(a)Put these words in order of probability, starting with the least likely.
unlikely certain evens impossible likely(1)

(b)A fair spinner has 4 equal sections. Only one section is yellow. On the probability scale, mark with a cross (X) the probability that the spinner lands on yellow.(1)

(c)On the same scale, mark with a circle (O) the probability that the spinner does not land on yellow.(1)

(Total for Question 2 is 3 marks)

A day of the week is chosen at random from the seven days Monday to Sunday.

(a)Write down the probability that the day chosen begins with the letter S.(1)

(b)Write down the probability that the day chosen is a weekday (Monday to Friday).(1)

(Total for Question 3 is 2 marks)

A letter is chosen at random from the word STATISTICS.

(a)Work out the probability that the letter chosen is S.(1)

(b)Work out the probability that the letter chosen is not a vowel.(1)

(Total for Question 4 is 2 marks)

A fair ten-sided dice, numbered 1 to 10, is rolled once.

(a)Write down the probability that the dice lands on a multiple of 3.(1)

(b)Work out the probability that the dice lands on a prime number.(1)

(Total for Question 5 is 2 marks)

A survey asked 80 students how they travel to school. The results are shown below.
Walk: 32 Bus: 24 Car: 16 Bike: 8
One of these students is chosen at random.

(a)Work out the probability that this student walks to school.(1)

(b)Work out the probability that this student does not travel by bus.(1)

(c)Work out the percentage of students who travel by car or by bike.(2)

(Total for Question 6 is 4 marks)

A bag contains 20 sweets. 8 are strawberry, 5 are lime, 4 are orange and the rest are blackcurrant. A sweet is taken from the bag at random.

(a)Work out the probability that the sweet is blackcurrant.(2)

(b)Work out the probability that the sweet is strawberry or lime.(1)

(Total for Question 7 is 3 marks)

A biased spinner can only land on red, blue, green or yellow. P(red) = 0.15, P(blue) = 0.3 and P(green) = 0.35.

(a)Work out P(yellow).(1)

(b)The spinner is spun 200 times. Work out an estimate for the number of times it lands on yellow.(2)

(Total for Question 8 is 3 marks)

The probability that Jamal buys a sandwich for lunch is 0.4. The probability that he buys a salad is 0.25. Jamal never buys both a sandwich and a salad on the same day.

(a)Work out the probability that Jamal buys a sandwich or a salad.(1)

(b)Work out the probability that Jamal buys neither a sandwich nor a salad.(1)

(Total for Question 9 is 2 marks)

A fair twelve-sided dice is numbered 1 to 12. It is rolled once.
Jake says: "The probability of rolling a factor of 12 is 5/12, because the factors are 1, 2, 3, 4 and 6."
Explain the error in Jake's reasoning and write down the correct probability.

(Total for Question 10 is 2 marks)

The probability that a customer at a cafe buys a hot drink is 0.6.

(a)Work out the probability that a customer does not buy a hot drink.(1)

(b)There are 45 customers at the cafe today. Work out an estimate for the number of these customers who buy a hot drink.(2)

(Total for Question 11 is 3 marks)

A weather forecaster says the probability that it will snow tomorrow is 0.1. It snows. Does this mean the weather forecaster was wrong? Give a reason for your answer.

(Total for Question 12 is 1 mark)

150 people at a leisure centre were asked whether they prefer swimming or the gym. The two-way table shows some of the information.

Figure (to be drawn): Two-way table with columns Swimming, Gym, Total and rows Adults, Children, Total. Adults: Swimming 38, Gym 52, Total 90. Children: Swimming (blank), Gym (blank), Total 60. Total: Swimming 70, Gym (blank), Total 150.

(a)Complete the two-way table.(3)

(b)One of these 150 people is chosen at random. Work out the probability that this person is a child who prefers the gym.(1)

(Total for Question 13 is 4 marks)

A spinner is spun different numbers of times. The table shows the number of times it lands on green.
Number of spins: 10, 50, 200, 500
Times landed on green: 3, 14, 62, 151

(a)Work out the relative frequency of landing on green after 500 spins.(1)

(b)Which of the four relative frequencies gives the best estimate of the probability that the spinner lands on green? Give a reason for your answer.(1)

(c)Using your estimate from part (b), work out an estimate for the number of times the spinner will land on green in 1000 spins.(2)

(Total for Question 14 is 4 marks)

Two fair four-sided dice, each numbered 1 to 4, are rolled together and the two scores are added to give a total.

(a)Work out the probability that the total is 5.(2)

(b)Work out the probability that the total is at least 7.(1)

(Total for Question 15 is 3 marks)

Priya has four number cards: 2, 5, 7 and 9. She picks two of the cards, without replacement, and places them side by side to make a two-digit number (the first card picked is the tens digit).

(a)List all the possible two-digit numbers Priya could make.(2)

(b)Priya picks two cards at random to make a number. Work out the probability that the number is even.(1)

(c)Work out the probability that the number is greater than 70.(2)

(Total for Question 16 is 5 marks)

A bag contains only red, blue and green counters, in the ratio 2 : 3 : 5. There are 60 counters in the bag altogether.

(a)Work out the number of green counters in the bag.(2)

(b)A counter is taken from the bag at random. Work out the probability that it is not blue.(2)

(Total for Question 17 is 4 marks)

A fair spinner can only land on red, blue or green. P(red) = 2 x P(blue). P(green) = 0.4.

(a)Work out P(blue).(2)

(b)Work out P(red).(1)

(Total for Question 18 is 3 marks)

Mark scheme · 2.12B Probability (Foundation) (Part 2)

Question 1

(a) B1 1 cao (accept 'certain')
(a) Answer: 1
(b) B1 0 cao (accept 'impossible')
(b) Answer: 0

Question 2

(a) B1 impossible, unlikely, evens, likely, certain (all five in the correct order)
(a) Answer: impossible, unlikely, evens, likely, certain
(b) B1 cross one quarter of the way along the scale (at 0.25), oe
(b) Answer: 0.25 (one quarter of the way along the scale)
(c) B1 circle three quarters of the way along the scale (at 0.75), oe, ft their (b)
(c) Answer: 0.75 (three quarters of the way along the scale)

Question 3

(a) B1 2/7 oe
(a) Answer: 2/7
(b) B1 5/7 oe
(b) Answer: 5/7

Question 4

(a) B1 3/10 oe
(a) Answer: 3/10
(b) B1 7/10 oe, ft their vowel count
(b) Answer: 7/10

Question 5

(a) B1 3/10 oe
(a) Answer: 3/10
(b) B1 2/5 oe (accept 4/10)
(b) Answer: 2/5

Question 6

(a) B1 2/5 oe (accept 32/80, 0.4, 40%)
(a) Answer: 2/5
(b) B1 7/10 oe (accept 56/80, 0.7, 70%)
(b) Answer: 7/10
(c) M1 16 + 8 (= 24), or 24/80 seen
(c) A1 30% cao
(c) Answer: 30%

Question 7

(a) M1 20 - 8 - 5 - 4 (= 3) to find the number of blackcurrant sweets
(a) A1 3/20 oe cao
(a) Answer: 3/20
(b) B1 13/20 oe
(b) Answer: 13/20

Question 8

(a) B1 0.2 cao (accept correct method 1 - 0.15 - 0.3 - 0.35)
(a) Answer: 0.2
(b) M1 0.2 x 200, ft their (a)
(b) A1 40 cao
(b) Answer: 40

Question 9

(a) B1 0.65 cao
(a) Answer: 0.65
(b) B1 0.35 oe, ft their (a)
(b) Answer: 0.35

Question 10

B1 identifies that Jake has missed a factor: 12 itself is also a factor of 12, so the factors are 1, 2, 3, 4, 6 and 12
B1 1/2 oe (accept 6/12) cao
Answer: Jake is wrong; the correct probability is 1/2 (he missed the factor 12).

Question 11

(a) B1 0.4 cao
(a) Answer: 0.4
(b) M1 0.6 x 45
(b) A1 27 cao
(b) Answer: 27

Question 12

B1 any valid reason, e.g. no, because a probability of 0.1 means the event is unlikely but still possible, so it can still happen
Answer: No, because an event with a probability of 0.1 is unlikely but not impossible, so it can still occur.

Question 13

(a) M1 70 - 38 (= 32) to find Children Swimming, or a correct method for another missing value
(a) M1 60 - 32 (= 28) to find Children Gym, or 52 + (their Children Gym) for the Gym total
(a) A1 all values correct: Children Swimming = 32, Children Gym = 28, Gym total = 80
(a) Answer: Children Swimming = 32, Children Gym = 28, Gym total = 80
(b) B1 14/75 oe (accept 28/150), ft their (a)
(b) Answer: 14/75

Question 14

(a) B1 0.302 oe (accept 151/500)
(a) Answer: 0.302
(b) B1 the relative frequency from 500 spins, because it is based on the greatest number of trials (a larger sample size gives a more reliable estimate)
(b) Answer: The relative frequency from 500 spins (0.302), because it uses the greatest number of trials.
(c) M1 0.302 x 1000, ft their (b) estimate
(c) A1 302 cao
(c) Answer: 302

Question 15

(a) M1 listing at least 3 of the 4 correct pairs (1,4) (2,3) (3,2) (4,1), or 4/16 seen
(a) A1 1/4 oe cao
(a) Answer: 1/4
(b) B1 3/16 oe, ft their method
(b) Answer: 3/16

Question 16

(a) M1 at least 6 correct, distinct two-digit numbers listed with a systematic attempt
(a) A1 all 12 numbers listed correctly with no repeats: 25, 27, 29, 52, 57, 59, 72, 75, 79, 92, 95, 97
(a) Answer: 25, 27, 29, 52, 57, 59, 72, 75, 79, 92, 95, 97
(b) B1 1/4 oe (accept 3/12), ft their (a)
(b) Answer: 1/4
(c) M1 identifies the 6 numbers greater than 70: 72, 75, 79, 92, 95, 97 (or an equivalent method)
(c) A1 1/2 oe cao
(c) Answer: 1/2

Question 17

(a) M1 60 / 10 (= 6) to find the value of one ratio part
(a) A1 30 cao
(a) Answer: 30
(b) M1 3 x 6 (= 18) to find the number of blue counters, or 60 - 18
(b) A1 7/10 oe cao (accept 42/60)
(b) Answer: 7/10

Question 18

(a) M1 3x + 0.4 = 1 oe, or 2x + x = 0.6 seen
(a) A1 0.2 cao
(a) Answer: 0.2
(b) B1 0.4 cao, ft 2 x their (a)
(b) Answer: 0.4

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Probability (Foundation) (Part 2) - Worksheets, Questions and Revision

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2.12B Probability (Foundation) (Part 2)

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