Conditional Probability (Foundation): Fluency and Exam Drill - Worksheets, Questions and Revision

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F08D Conditional Probability (Foundation): Fluency and Exam Drill

EDEXCEL 1ST0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down what P(A|B) means in words.

(Total for Question 1 is 1 mark)

P(X and Y) = 0.3 and P(Y) = 0.6. Write down the formula used to find P(X|Y).

(Total for Question 2 is 1 mark)

A bag contains 5 red and 3 blue counters. One counter is removed and not replaced. Write down how many counters remain in the bag.

(Total for Question 3 is 1 mark)

A bag contains 6 red and 4 green sweets. A red sweet is removed and eaten. Write down how many red sweets remain in the bag.

(Total for Question 4 is 1 mark)

State whether the following are independent or dependent events: rolling a fair dice, then rolling it again.

(Total for Question 5 is 1 mark)

State whether the following are independent or dependent events: picking two cards from a deck, one after another, without replacing the first.

(Total for Question 6 is 1 mark)

For events A and B, P(A) = 0.4 and P(A|B) = 0.4. Write down whether A and B are independent, giving a brief reason.

(Total for Question 7 is 1 mark)

60 people were asked whether they own a bike and whether they own a car. The two-way table shows the results.

	Car	No car	Total
Bike	12	18	30
No bike	20	10	30
Total	32	28	60

One person is chosen at random from those who own a bike. Find the probability that this person also owns a car.

(Total for Question 8 is 2 marks)

50 students were asked whether they study French and whether they study Spanish. The two-way table shows the results.

	Spanish	No Spanish	Total
French	9	16	25
No French	11	14	25
Total	20	30	50

One student is chosen at random from those who study Spanish. Find the probability that this student also studies French.

(Total for Question 9 is 2 marks)

A bag contains 12 marbles: 7 blue and 5 orange. Priti takes a marble at random from the bag and does not replace it. The marble she took was blue. Find the probability that the second marble she takes is also blue.

(Total for Question 10 is 2 marks)

A drawer contains 10 socks: 6 black and 4 white. Tom takes a sock at random and does not replace it. The sock he took was white. Find the probability that the second sock he takes is black.

(Total for Question 11 is 2 marks)

80 customers at a cafe were asked whether they bought a hot drink and whether they bought a cake. The two-way table shows the results.

	Cake	No cake	Total
Hot drink	24	26	50
No hot drink	6	24	30
Total	30	50	80

One customer is chosen at random from those who bought a cake. Find the probability that this customer also bought a hot drink.

(Total for Question 12 is 2 marks)

45 members of a gym were asked whether they attend yoga classes and whether they attend spin classes. The two-way table shows the results.

	Spin	No spin	Total
Yoga	6	15	21
No yoga	14	10	24
Total	20	25	45

One member is chosen at random from those who attend spin classes. Find the probability that this member does not attend yoga.

(Total for Question 13 is 2 marks)

90 people were asked whether they have a season ticket or pay per visit at a swimming pool. The two-way table shows some of the results.

	Season ticket	Pay per visit
Adults	22	\| 50
Children	\| 18	40
Total	\|	90

(a)Complete the two-way table.(2)

(b)One person is chosen at random from those who pay per visit. Find the probability that this person is an adult.(1)

(Total for Question 14 is 3 marks)

A jar contains 15 sweets: 9 orange and 6 lime. Deepa takes a sweet at random from the jar and eats it. She does not replace it. The sweet Deepa took was lime.

(a)Find the probability that the second sweet Deepa takes is also lime.(2)

(b)Find the probability that the second sweet Deepa takes is orange.(1)

(Total for Question 15 is 3 marks)

For two events C and D, P(C) = 0.3, P(D) = 0.6 and P(C and D) = 0.18.

(a)Use the formula P(C|D) = P(C and D) / P(D) to find P(C|D).(2)

(b)Determine, giving a reason, whether events C and D are independent.(1)

(Total for Question 16 is 3 marks)

A box contains 10 balls, numbered 1 to 10. Marcus takes a ball at random from the box and does not replace it. He then takes a second ball at random from the box.

(a)Given that the first ball shows an odd number, find the probability that the second ball also shows an odd number.(2)

(b)Find the probability that both balls show odd numbers.(2)

(Total for Question 17 is 4 marks)

240 students travel to a college by either train or bike. Of the 150 who travel by train, 24 arrive late. Of the 90 who travel by bike, 18 arrive late.

(a)Write down the total number of students who arrive late.(1)

(b)A student is chosen at random from those who arrive late. Find the probability that this student travels by bike.(2)

(Total for Question 18 is 3 marks)

A student carries out a statistics project investigating whether pupils who attend a weekly coding club are more likely to be placed in the school's top maths set.

(a)Write a suitable hypothesis for this investigation.(1)

(b)The student plans to collect data only from members of the coding club. Give one reason why this sampling method could make the investigation's conclusions unreliable.(1)

(c)The student instead surveys 80 pupils across the whole school. The two-way table shows the results.

	Top set	Not top set	Total
Coding club	18	12	30
Not coding club	15	35	50
Total	33	47	80

Find P(top set | coding club) and P(top set | not coding club).(2)

(d)Using your answers to part (c), comment on whether the data supports the hypothesis, and give one limitation of this conclusion.(1)

(Total for Question 19 is 5 marks)

Mark scheme · F08D Conditional Probability (Foundation): Fluency and Exam Drill

Question 1

B1 the probability of A given that B has happened, oe
Answer: The probability of A, given that B has happened.

Question 2

B1 P(X|Y) = P(X and Y) / P(Y), oe
Answer: P(X|Y) = P(X and Y) / P(Y)

Question 3

B1 7 cao
Answer: 7

Question 4

B1 5 cao
Answer: 5

Question 5

B1 Independent cao
Answer: Independent

Question 6

B1 Dependent cao
Answer: Dependent

Question 7

B1 Independent, since P(A|B) = P(A), oe
Answer: Independent, since P(A|B) = P(A) = 0.4.

Question 8

M1 12/30 seen, oe
A1 2/5 oe cao
Answer: 2/5

Question 9

M1 9/20 seen, oe
A1 9/20 oe cao
Answer: 9/20

Question 10

M1 6/11 seen (6 blue marbles remain out of 11 left)
A1 6/11 cao
Answer: 6/11

Question 11

M1 6/9 seen (6 black socks remain out of 9 left)
A1 2/3 oe cao
Answer: 2/3

Question 12

M1 24/30 seen, oe
A1 4/5 oe cao
Answer: 4/5

Question 13

M1 14/20 seen, oe
A1 7/10 oe cao
Answer: 7/10

Question 14

(a) M1 at least two of the four missing values found
(a) A1 all four correct: Adults pay per visit = 28, Children season ticket = 22, Total season ticket = 44, Total pay per visit = 46
(a) Answer: Adults pay per visit = 28; Children season ticket = 22; Total season ticket = 44; Total pay per visit = 46
(b) B1 14/23 oe cao (ft from part (a))
(b) Answer: 14/23

Question 15

(a) M1 5/14 seen (5 lime sweets remain out of 14 left)
(a) A1 5/14 cao
(a) Answer: 5/14
(b) B1 9/14 cao
(b) Answer: 9/14

Question 16

(a) M1 0.18 / 0.6, oe
(a) A1 0.3 cao
(a) Answer: 0.3
(b) B1 Independent, since P(C|D) = 0.3 = P(C), oe (equivalently P(C) x P(D) = 0.18 = P(C and D))
(b) Answer: Independent, since P(C|D) = 0.3, which equals P(C).

Question 17

(a) M1 identifies 5 odd numbers in total, so 4 remain out of 9 balls left
(a) A1 4/9 oe cao
(a) Answer: 4/9
(b) M1 5/10 x 4/9, oe
(b) A1 2/9 oe cao
(b) Answer: 2/9

Question 18

(a) B1 42 cao
(a) Answer: 42
(b) M1 18/42 seen, oe
(b) A1 3/7 oe cao
(b) Answer: 3/7

Question 19

(a) B1 a clear, testable hypothesis linking coding club attendance with top-set placement, e.g. 'Pupils who attend the coding club are more likely to be in the top maths set'
(a) Answer: Pupils who attend the coding club are more likely to be in the top maths set (accept any equivalent testable statement).
(b) B1 identifies bias, e.g. coding club members already share an interest so there is no fair comparison group, or the sample is not representative of the whole school, oe
(b) Answer: Sampling only coding club members is biased: it excludes pupils who do not attend the club, so there is no fair comparison group and the sample may not represent the whole school.
(c) M1 18/30 and 15/50 identified
(c) A1 3/5 oe and 3/10 oe, both cao
(c) Answer: P(top set | coding club) = 3/5; P(top set | not coding club) = 3/10
(d) B1 supports the hypothesis since 3/5 (0.6) is greater than 3/10 (0.3), together with a valid limitation, e.g. the sample of 80 pupils from one school may not represent all pupils, or an association does not prove that one causes the other, oe
(d) Answer: The data supports the hypothesis, since 3/5 (0.6) is greater than 3/10 (0.3): pupils who attend the coding club are more likely to be in the top set. Limitation: this is a sample of 80 pupils from one school, and an association does not prove that one causes the other.

Question 19

5 marks

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Conditional Probability (Foundation): Fluency and Exam Drill - Worksheets, Questions and Revision

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