Probability Trees: Fluency and Exam Drill - Worksheets, Questions and Revision

20 original exam-style questions - 15 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Statistics and Probability

5.22D Probability Trees: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 85 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
State whether each statement about probability tree diagrams is True or False.
(a)The probabilities on each pair of branches leading from the same point on a tree diagram must add up to 1.(1)
  • True
  • False
(b)To find the probability of a combined outcome along a single path through a tree diagram, you multiply the probabilities along that path.(1)
  • True
  • False
(c)When counters are removed from a bag and not replaced, the probabilities on the second set of branches are always identical to the probabilities on the first set of branches.(1)
  • True
  • False
(d)To find the probability that either of two different, mutually exclusive routes through a tree diagram occurs, you add the two route probabilities.(1)
  • True
  • False
(Total for Question 1 is 4 marks)
2
A biased spinner can only land on Win or Lose. The probability that it lands on Win is 0.35.
Spin 1 Spin 2 Start 0.35 Win Lose Win Lose Win Lose (Not to scale)
(a)Write down the probability that the spinner lands on Lose.(1)
(b)The spinner is spun twice. The probability tree diagram shows the first spin, with all four second-stage branches left blank. Complete the tree diagram by writing the correct probability on each of the four second-stage branches.(2)
(Total for Question 2 is 3 marks)
3
A fair six-sided dice is rolled twice. Calculate the probability of getting a 6 on both rolls.
(Total for Question 3 is 2 marks)
4
The probability that it snows on any given day in December this year is 0.1, independently of other days. Two December days are chosen at random.
(a)Write down the probability that it does not snow on a given day.(1)
(b)Calculate the probability that it snows on both days.(2)
(Total for Question 4 is 3 marks)
5
A jar contains 4 lemon sweets and 2 orange sweets only. Declan takes a sweet at random from the jar and does not replace it. He then takes a second sweet at random. The probability tree diagram shows the first draw, with all four second-stage branches left blank. Complete the tree diagram by writing the correct probability, as a fraction, on each of the four second-stage branches.
Draw 1 Draw 2 4/6 2/6 Lemon Orange Lemon Orange Lemon Orange (Not to scale)
(Total for Question 5 is 2 marks)
6
The probability that Leon's football team wins any given match is 0.3, independently of other matches. Consider the team's next two matches.
Match 1 Match 2 Win 0.3 0.7 Not win Win Not win Win Not win Diagram NOT to scale
(a)Complete the probability tree diagram for the two matches by writing the missing probability on each of the four second-stage branches.(2)
(b)Calculate the probability that the team wins exactly one of the two matches.(3)
(c)Calculate the probability that the team wins at least one of the two matches.(3)
(Total for Question 6 is 8 marks)
7
A pencil case contains 5 blue pens and 4 black pens only. Ravi takes a pen at random from the pencil case and does not put it back. He then takes a second pen at random.
Draw 1 Draw 2 5/9 4/9 Blue Black Blue Black Blue Black (Not to scale)
(a)Complete the probability tree diagram, writing each missing probability as a fraction.(2)
(b)Calculate the probability that both pens are blue.(2)
(c)Calculate the probability that the two pens are different colours.(3)
(Total for Question 7 is 7 marks)
8
On any given day, the probability that Jamal passes his driving theory mock test is 0.8. The probability that he passes his practical mock test is 0.75. The results of the two mock tests are independent of each other.
(a)Find the probability that Jamal passes both mock tests.(2)
(b)Find the probability that Jamal passes exactly one of the two mock tests.(3)
(Total for Question 8 is 5 marks)
9
Tunde buys 2 raffle tickets from a box of 40 tickets, 5 of which are winning tickets.
(a)Find the probability that both of Tunde's tickets are winning tickets.(2)
(b)Find the probability that neither of Tunde's tickets is a winning ticket.(2)
(Total for Question 9 is 4 marks)
10
A jar contains 6 green marbles and 3 orange marbles only. Ola takes a marble at random from the jar and does not replace it. She then takes a second marble at random.
Draw 1 Draw 2 6/9 3/9 Green Orange Green Orange Green Orange (Not to scale)
(a)Complete the probability tree diagram, writing each missing probability as a fraction.(2)
(b)Calculate the probability that both marbles are the same colour.(3)
(c)Calculate the probability that at least one of the two marbles is orange.(3)
(Total for Question 10 is 8 marks)
11
A gardener plants 4 sunflower seeds. Each seed germinates independently with probability 0.9. Find the probability that at least one of the seeds fails to germinate.
(Total for Question 11 is 3 marks)
12
Aisha plays a game against a computer program twice. In each game, independently, the probability she Wins is 0.5, the probability of a Draw is 0.3, and the probability she Loses is 0.2.
(a)Find the probability that Aisha wins both games.(2)
(b)Find the probability that Aisha gets one Win and one Draw, in either order.(3)
(Total for Question 12 is 5 marks)
13
A library shelf holds 8 fiction books and 12 non-fiction books only. Sophie picks two books from the shelf at random, one after another, without replacement.
Book 1 Book 2 8/20 12/20 Fiction Non-fiction Fiction Non-fiction Fiction Non-fiction (Not to scale)
(a)Complete the probability tree diagram, writing each missing probability as a fraction.(2)
(b)Calculate the probability that both books are fiction.(2)
(c)Calculate the probability that exactly one of the two books is fiction.(3)
(Total for Question 13 is 7 marks)
14
A fruit basket contains 10 apples and 5 oranges only. Two pieces of fruit are taken from the basket at random, one after another, without replacement. Find the probability that at least one apple is taken.
(Total for Question 14 is 3 marks)
15
Server 1 and Server 2 at a small company operate independently of each other. On any given day, the probability that Server 1 fails is 0.08. The probability that Server 2 fails is 0.05.
Server 1 Server 2 Fails Does not fail 0.08 0.92 Fails Does not fail Fails Does not fail (Diagram NOT to scale)
(a)Complete the probability tree diagram for a single day, showing both servers.(2)
(b)Calculate the probability that exactly one of the two servers fails on a given day.(3)
(Total for Question 15 is 5 marks)
16
A footballer takes three penalties in training. Each penalty is scored independently with probability 0.75. Calculate the probability that she scores exactly 2 of the 3 penalties.
(Total for Question 16 is 3 marks)
17
A box contains 7 red discs and 5 yellow discs only. Mei takes a disc at random from the box and does not replace it. She then takes a second disc at random.
Disc 1 Disc 2 7/12 5/12 Red Yellow Red Yellow Red Yellow (Not to scale)
(a)Complete the probability tree diagram, writing each missing probability as a fraction.(2)
(b)Given that the first disc Mei takes is red, write down the probability that the second disc is yellow.(1)
(c)Calculate the probability that the two discs are different colours.(3)
(Total for Question 17 is 6 marks)
18
A box contains 3 winning raffle tickets and 17 non-winning tickets only. Callum takes two tickets from the box at random, one after another, without replacement. Find the probability that at least one of Callum's tickets is a winning ticket.
(Total for Question 18 is 3 marks)
19
A rare medical condition affects 2% of a population. A screening test is used: if a person has the condition, the test correctly gives a positive result 96% of the time; if a person does not have the condition, the test incorrectly gives a positive result (a false positive) 4% of the time. A person is chosen at random from the population and given the test.
0.02 0.98 Condition No condition Test positive Test negative Test positive Test negative (Diagram NOT to scale)
(a)Complete the probability tree diagram for the randomly chosen person.(3)
(b)Calculate the probability that the person's test result is positive.(3)
(c)The person's test result is positive. Find the probability that they actually have the condition.(3)
(Total for Question 19 is 9 marks)
20
A bag contains 4 gold discs and n silver discs only, where n > 0. Two discs are taken from the bag at random, one after another, without replacement.
(a)Show that the probability that both discs are gold is 12 / ((n+4)(n+3)).(3)
(b)Given that the probability that both discs are gold is 2/15, show that n2 + 7n - 78 = 0.(2)
(c)Hence find the number of silver discs in the bag.(3)
(Total for Question 20 is 8 marks)
Mark scheme · 5.22D Probability Trees: Fluency and Exam Drill

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

Question 19

Question 20