Probability Revision Levels 7-9
The following questions have been taken from BBC Bitesize.
Please complete the two revision links below before attempting the questions if you’re unsure.
• http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/probability1rev1.shtml
• http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/probabilityhirev1.shtml
1.There are 20 counters in a box. Nine are yellow, 4 are black and 7 are green. What's the
probability that a counter that is taken from the box without looking will be green?
a) 7/20
b) 9/20
c) 4/20
2.What's the probability that a counter taken from the box without looking will be yellow or
black?
a) 7/20
b) 36/400
c) 13/20
3.What's the probability that a counter taken from the box without looking will be blue?
a) 0
b) Infinity
c) 1
4.What's the probability that a counter taken from the box without looking will not be black or
green?
a) 7/20
b) 9/20
c) 1/4
5.Two 6-sided dice are each marked 1, 1, 2, 2, 3, 3. Jot down all the possible pairs of numbers
that you can get when the two dice are thrown. The pairs of numbers are added together to get
a score. As the dice are only marked from 1-3, there's maximum score of 6.
What's the probability of getting a score of 3?
a) 2/9
b) 1/18
c) 1/9
6.What's the most likely score?
a) 3
b) 4
c) 5
7.What's the probability of getting a score of 6?
a) 1/36
b) 1/9
c) 2/9
8.Melanie has been recording how many times a drawing pin landed point-up after being thrown
in the air. She threw the pin 50 times and found it landed point-up 9 times. What's the
probability of it landing point-up in the next throw?
a) 9/50
b) 1/2
c) 1/50
9.What's the probability it doesn't land point-up after the next throw?
a) 49/50
b) 1/2
c) 41/50
10.The next day she throws the drawing pin in the air 200 times. Using her figures from the
previous day, roughly how many times could she expect the drawing pin to land point-up?
a) 45
b) 27
c) 36
Drawer A contains 7 red socks and 3 black socks.!
Drawer B contains 4 red socks and 6 black socks.
A sock is taken from each drawer.
Copy the tree diagram and find the values of A, B and C.
11. A = ?
12. B = ?
13. C = ?
14. What's the probability of taking two red socks?
15. What's the probability of taking a sock of each colour?
Tom likes to lie in bed in the morning.
The probability that he's late for school is 0.1.
Draw a tree diagram to represent the probabilities of Tom being late on Monday, Tuesday and
Wednesday.
6. What's the probability that he's late on all three mornings?
19. What's the probability of obtaining one red bead?
7. What's the probability that he's late on Monday and Tuesday, but on time on Wednesday?
20. What's the probability of obtaining at least one red bead?
8. What's the probability that he's late on only one of the three mornings?
21. In a standard deck of 52 playing cards, find the following probabilities.
Two dice are biased so that the probability of getting a six on each die is 0.2.
The two dice are rolled. By drawing a tree diagram, or otherwise, find:
(a) Pr(jack)
9. P(two 6s)
(b) Pr(black 7)
(c) Pr(heart)
10. P(exactly one 6)
11.Two dice are rolled. The events 'obtaining a six with the first die' and 'obtaining an even
number with the second die' are independent.
True
False
12.A box contains 7 red balls and 4 white balls. Two balls are taken out and not replaced. The
events 'the first ball is red' and 'the second ball is white' are independent.
True
False
13.A bag contains 3 green counters and 6 black counters. A counter is taken from the bag, its
colour noted, and then replaced. A second counter is then taken from the bag. The events 'the
first counter is green' and 'the second counter is black' are independent.!
True
False
A bag contains 2 red beads and 3 black beads. Two beads are
taken from the bag and not replaced.
22. A die is rolled and a coin is tossed.
(a) Draw a two-way table to list all possible outcomes.
(b) From the table in part (a), calculate the probability of obtaining a head and an even number.
23. The following Venn diagram shows students who play
the piano (P) and play the guitar (G). If one person is
chosen at random, find the probability that:
(a) a student plays guitar
(b) a student plays piano but not guitar
(c) a student plays both instruments.
24.Use the following Venn diagram to find:
14. P =
15. Q =
(a) number of people surveyed
(b) Pr (M or F)
16. R =
17. S =
18. What's the probability that both beads are the same colour?
(c) Pr (not F)