Probability Exam Questions Q1. There are 52 cards in a pack. 12 cards are picture cards. 40 cards are number cards. Melina takes at random a card from the pack. She keeps the card and then takes at random a second card from the remainder of the pack. (a) Complete the probability tree diagram. (3) (b) Work out the probability that the two cards Melina takes are both picture cards or both number cards. ........................................................... (3) (Total for question = 6 marks)
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Probability Exam Questions Q1.
There are 52 cards in a pack. 12 cards are picture cards. 40 cards are number cards.
Melina takes at random a card from the pack. She keeps the card and then takes at random a second card from the remainder of the pack.
(a) Complete the probability tree diagram.
(3)
(b) Work out the probability that the two cards Melina takes are both picture cards or both number cards.
...........................................................
(3)
(Total for question = 6 marks)
Q2.
Naveed has two bags of tiles, bag A and bag B.
There are 10 tiles in bag A. 7 of these tiles are red. The other 3 tiles are white.
There are 8 tiles in bag B. 5 of these tiles are red. The other 3 tiles are white.
Naveed takes at random one tile from each bag.
(a) Work out the probability that the tiles are the same colour.
...........................................................
(3)
All 18 tiles are put in a box. Naveed takes at random one tile from the box. He does not replace the tile. Naveed then takes at random a second tile from the box.
(b) Work out the probability that both tiles are red.
...........................................................
(2)
(Total for question = 5 marks)
Q3. (Look at the number of marks…. Use this to help to simplify the problem)
The diagram shows three boxes containing beads.
Each box contains 3 black beads and 6 white beads.
Tim takes at random a bead from box A and puts it into box B. He then takes at random a bead from box B and puts it into box C. Finally, he takes at random a bead from box C and puts it into box A.
Calculate the probability that there are still 3 black beads and 6 white beads in each of the three boxes.
...........................................................
(Total for question = 3 marks) Q4.
A bag contains 12 marbles. 6 of the marbles are red, 4 of the marbles are blue and 2 of the marbles are green.
Raj takes at random 3 marbles from the bag.
Find the probability that exactly 2 of these marbles are blue.
...........................................................
(Total for question = 3 marks)
Q5.
Gemma has 9 counters. Each counter has a number on it.
Gemma puts the 9 counters into a bag. She takes at random a counter from the bag and does not replace the counter. She then takes at random a second counter from the bag.
(a) Work out the probability that the number on each counter is an even number.
...........................................................
(2)
(b) Work out the probability that the number on the first counter added to the number on the second counter gives an odd number.
...........................................................
(3)
(Total for question = 5 marks)
Q6.
Here are seven counters. Each counter has a number on it.
Ali puts the seven counters in a bag. He takes, at random, a counter from the bag and does not replace the counter. He then takes, at random, a second counter from the bag. Calculate the probability that (i) the number on the second counter is 2 more than the number on the first counter,
...........................................................
(ii) the number on the second counter is 1 more than the number on the first counter.
...........................................................
(Total for question = 5 marks)
Q7.
There are 12 sweets in a bag.
4 of the sweets are lemon flavour. 4 of the sweets are strawberry flavour. 4 of the sweets are orange flavour.
Luke takes at random 3 of the sweets.
Work out the probability that exactly 2 of the sweets that Luke takes are the same flavour.
...........................................................
(Total for question = 5 marks)
Q8.
Here are ten counters. Each counter has a number on it.
Fern puts the ten counters in a bag. She takes at random a counter from the bag. (a) Find the probability that the number on the counter is 3 or 4
........................................................... (2)
Fern puts the counter back into the bag. Then Rajan takes at random one of the ten counters from the bag. He does not put the counter back into the bag. He then takes at random a second counter from the bag. (b) Calculate the probability that 3 is the number on each of the two counters he takes.
........................................................... (2)
(c) Calculate the probability that the sum of the numbers on the two counters he takes is an odd number.
........................................................... (3)
(Total for question = 7 marks)
Q9.
There are 9 counters in a bag. There is a number on each counter.
Kal takes at random 3 counters from the bag.
He adds together the numbers on the 3 counters to get his Total.
Work out the probability that his Total is 6
...........................................................
(Total for question = 5 marks)
Extension Question Q10.
There are 7 red counters in a bag. The rest of the counters in the bag are blue.
There are more blue counters than red counters in the bag.
Two counters are to be taken at random from the bag.
The probability that there will be one counter of each colour is
Work out the total number of counters in the bag before any counters are taken from the bag.
...........................................................
(Total for question = 5 marks)
Mark Scheme Q1.
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