GCSE Probability

1.	Julie does a statistical experiment. She throws a dice 600 times.
She scores six 200 times.
(a)	Is the dice fair? Explain your answer.
(1)
	Julie then throws a fair red dice once and a fair blue dice once.
(b)	Complete the probability tree diagram to show the outcomes.
Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.

(3)
(Total 4 marks)
2.	A bag contains 3 black beads, 5 red beads and 2 green beads.
Gianna takes a bead at random from the bag, records its colour and replaces it.
She does this two more times.
	Work out the probability that, of the three beads Gianna takes, exactly two are
the same colour.
(Total 5 marks)
3.	Julie does a statistical experiment. She throws a dice 600 times.
She scores six 200 times.
(a)	Is the dice fair? Explain your answer.
(1)
	Julie then throws a fair red dice once and a fair blue dice once.
(b)	Complete the probability tree diagram to show the outcomes.
Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.

(3)
(c)	(i)	Julie throws a fair red dice once and a fair blue dice once. Calculate the probability that Julie gets a six on both the red dice and the blue dice.
(ii)	Calculate the probability that Julie gets at least one six.
(5)
(Total 9 marks)
4.	The probability that Betty will be late for school tomorrow is 0.05
The probability that Colin will be late for school tomorrow is 0.06
	The probability that both Betty and Colin will be late for school tomorrow is 0.011
	Fred says that the events ‘Betty will be late tomorrow’ and ‘Colin will be late tomorrow’ are independent.
	Justify whether Fred is correct or not.
(Total 2 marks)
5.	Martin has a pencil case which contains 4 blue pens and 3 green pens.
	Martin picks a pen at random from the pencil case. He notes its colour, and then replaces it.
He does this two more times.
	Work out the probability that when Martin takes three pens, exactly two are the same colour.
(Total 3 marks)
6.	Phil has 20 sweets in a bag.
	5 of the sweets are orange.
7 of the sweets are red.
8 of the sweets are yellow.
	Phil takes at random two sweets from the bag.
	Work out the probability that the sweets will not be the same colour.
(Total 4 marks)
7.	In a game of chess, a player can either win, draw or lose.
	The probability that Vishi wins any game of chess is 0.5
The probability that Vishi draws any game of chess is 0.3
	Vishi plays 2 games of chess.
(a)	Complete the probability tree diagram.

(2)
(b)	Work out the probability that Vishi will win both games.
(2)
(Total 4 marks)
8.	Matthew puts 3 red counters and 5 blue counters in a bag.
He takes at random a counter from the bag.
He writes down the colour of the counter.
He puts the counter in the bag again.
He then takes at random a second counter from the bag.
(a)	Complete the probability tree diagram.

(2)
(b)	Work out the probability that Matthew takes two red counters.
(2)
(Total 4 marks)
9.	Tom and Sam each take a driving test.
	The probability that Tom will pass the driving test is 0.8
	The probability that Sam will pass the driving test is 0.6
(a)	Complete the probability tree diagram.
		
(2)
(b)	Work out the probability that both Tom and Sam will pass the driving test.
(2)
(c)	Work out the probability that only one of them will pass the driving test.
(3)
(Total 7 marks)

10.	Julie has 100 music CDs.
58 of the CDs are classical.
22 of the CDs are folk.
The rest of the CDs are jazz.
	On Saturday, Julie chooses one CD at random from the 100 CDs.
On Sunday, Julie chooses one CD at random from the 100 CDs.
(a)	Complete the probability tree diagram.
(2)
 
(b)	Calculate the probability that Julie will choose a jazz CD on both Saturday and
Sunday.
(3)
(Total 7 marks)
11.	Joan has two boxes of chocolates.
The boxes are labelled A and B.
	Box A contains 15 chocolates. There are 6 plain, 4 milk and 5 white chocolates.
Box B contains 12 chocolates. There are 4 plain, 3 milk and 5 white chocolates.
	Joan takes one chocolate at random from each box.
Work out the probability that the two chocolates Joan takes are not of the same type.
(Total 4 marks)
12.	There are two sets of traffic lights on Georgina’s route to school.
The probability that the first set of traffic lights will be red is 0.4
The probability that the second set of traffic lights will be red is 0.3
(a)	Complete the probability tree diagram.

(2)
(b)	Work out the probability that both sets of traffic lights will be red.
(2)
(c)	Work out the probability that exactly one set of traffic lights will be red.
(3)
(Total 7 marks)
13.	The probability that any piece of buttered toast will land buttered side down when it is dropped is 0.62
Two pieces of buttered toast are to be dropped, one after the other.
	Calculate the probability that exactly one piece of buttered toast will land buttered side down.
(Total 4 marks)
14.	Mary has a drawing pin.
When the drawing pin is dropped it can land either ‘point up’ or ‘point down’.
The probability of it landing ‘point up’ is 0.4
	Mary drops the drawing pin twice.
(a)	Complete the probability tree diagram.

(2)
(b)	Work out the probability that the drawing pin will land ‘point up’ both times.
(2)
(Total 4 marks)
15.	Simon plays one game of tennis and one game of snooker.
	The probability that Simon will win at tennis is 
	The probability that Simon will win at snooker is 
(a)	Complete the probability tree diagram below.

(2)
(b)	Work out the probability that Simon wins both games.
(2)
(c)	Work out the probability that Simon will win only one game.
(3)
(Total 7 marks)
16.	Simon plays one game of tennis and one game of snooker.
	The probability that Simon will win at tennis is 
	The probability that Simon will win at snooker is 
	Complete the probability tree diagram.

(Total 2 marks)
17.	Loren has two bags.
The first bag contains 3 red counters and 2 blue counters.
The second bag contains 2 red counters and 5 blue counters.
	Loren takes one counter at random from each bag.
(a)	Complete the probability tree diagram.

(2)
(b)	Work out the probability that Loren takes one counter of each colour.
(3)
(Total 5 marks)
18.	Loren has two bags.
The first bag contains 3 red counters and 2 blue counters.
The second bag contains 2 red counters and 5 blue counters.
	Loren takes one counter at random from each bag.
	Complete the probability tree diagram.

(Total 2 marks)
19.	Jeremy designs a game for a school fair.
	He has two 5-sided spinners.
	The spinners are equally likely to land on each of their sides.
	One spinner has 2 red sides, 1 green side and 2 blue sides.
	The other spinner has 3 red sides, 1 yellow side and 1 blue side.
(a)	Calculate the probability that the two spinners will land on the same colour.
(3)

	The game consists of spinning each spinner once.
	It costs 20p to play the game.
	To win a prize both spinners must land on the same colour.
	The prize for a win is 50p.
	100 people play the game.
(b)	Work out an estimate of the profit that Jeremy should expect to make.
(2)
(Total 5 marks)
20.	Amy is going to play one game of snooker and one game of billiards.
	The probability that she will win the game of snooker is 
	The probability that she will win the game of billiards is 
(a)	Complete the probability tree diagram.

(2)
(b)	Work out the probability that Amy will win exactly one game.
(3)
	Amy played one game of snooker and one game of billiards on a number of Fridays.
She won at both snooker and billiards on 21 Fridays.
(c)	Work out an estimate for the number of Fridays on which Amy did not win either game.
(3)
(Total 8 marks)
21.	Amy is going to play one game of snooker and one game of billiards.
	The probability that she will win the game of snooker is 
	The probability that she will win the game of billiards is 
	Complete the probability tree diagram.

(Total 2 marks)
22.	In a game of chess, you can win, draw or lose.
	Gary plays two games of chess against Mijan.
	The probability that Gary will win any game against Mijan is 0.55
The probability that Gary will win draw game against Mijan is 0.3
(a)	Work out the probability that Gary will win exactly one of the two games against Mijan.
(3)
	In a game of chess, you score
	1 point for a win
	point for a draw,
	0 points for a loss.
(b)	Work out the probability that after two games, Gary’s total score will be the same as Mijan’s total score.
(3)
(Total 6 marks)
23.	Tony throws a biased dice 100 times.
The table shows his results.
Score	Frequency	
1	12	
2	13	
3	17	
4	10	
5	18	
6	30	
	He throws the dice once more.

(a)	Find an estimate for the probability that he will get a 6.
(1)
	Emma has a biased coin.
The probability that the biased coin will land on a head is 0.7
Emma is going to throw the coin 250 times.
(b)	Work out an estimate for the number of times the coin will land on a head.
(2)
(Total 3 marks)
24.	Amy has 10 CDs in a CD holder.
Amy’s favourite group is Edex.
She has 6 Edex CDs in the CD holder.
	Amy takes one of these CDs at random.
She writes down whether or not it is an Edex CD.
She puts the CD back in the holder.
Amy again takes one of these CDs at random.
(a)	Complete the probability tree diagram.

(2)
(b)	Find the probability that Amy will pick two Edex CDs.
(2)
	Amy had 30 CDs.
The mean playing time of these 30 CDs was 42 minutes.
	Amy sold 5 of her CDs.
The mean playing time of the 25 CDs left was 42.8 minutes.
(c)	Calculate the mean playing time of the 5 CDs that Amy sold.
(3)
(Total 7 marks)
25.	The probability that a biased dice will land on a four is 0.2
	Pam is going to roll the dice 200 times.
	The probability that a biased dice will land on a six is 0.4
Ted rolls the biased dice once.
	Work out the probability that the dice will land on either a four or a six.
(Total 2 marks)
26.	Amy has 10 CDs in a CD holder.
Amy’s favourite group is Edex.
She has 6 Edex CDs in the CD holder.
	Amy takes one of these CDs at random.
She writes down whether or not it is an Edex CD.
She puts the CD back in the holder.
Amy again takes one of these CDs at random.
(a)	Complete the probability tree diagram.

(2)
	Amy had 30 CDs.
The mean playing time of these 30 CDs was 42 minutes.
	Amy sold 5 of her CDs.
The mean playing time of the 25 CDs left was 42.8 minutes.
(b)	Calculate the mean playing time of the 5 CDs that Amy sold.
(3)
(Total 5 marks)