CAMBRIDGE IGCSE MATHS (0580)

Question 1:
A bag contains 7 white beads and 5 red beads.
Two beads are taken out of the bag at random, without replacement.
Find the probability that:
(a) they are both white,
(b) one is white and one is red.

Question 2:
(a) A square spinner is biased.
The probabilities of obtaining the scores 1, 2, 3, and 4 when it is spun are given in the table.

Score	1	2	3	4
Probability	0.1	0.2	0.4	0.3

(i) Work out the probability that on one spin the score is 2 or 3.
Answer(a)(i) ................................................ [2]
(ii) In 5000 spins, how many times would you expect to score 4 with this spinner?
Answer(a)(ii) ................................................ [1]
(iii) Work out the probability of scoring 1 on the first spin and 4 on the second spin.
Answer(a)(iii) ................................................ [2]
(b) In a bag there are 7 red discs and 5 blue discs.
From the bag a disc is chosen at random and not replaced.
A second disc is then chosen at random.
Work out the probability that at least one of the discs is red.
Give your answer as a fraction.
Answer(b) ................................................ [3]

Question 3:
In this question, give all your answers as fractions.


The letters of the word NATION are printed on 6 cards.
(a) A card is chosen at random.
Write down the probability that:
(i) it has the letter T printed on it,
Answer(a)(i) ................................................ [1]
(ii) it does not have the letter N printed on it,
Answer(a)(ii) ................................................ [1]
(iii) the letter printed on it has no lines of symmetry.
Answer(a)(iii) ................................................ [1]
(b) Lara chooses a card at random, replaces it, then chooses a card again.
Calculate the probability that only one of the cards she chooses has the letter N printed on it.
Answer(b) ................................................ [3]
(c) Jacob chooses a card at random and does not replace it.
He continues until he chooses a card with the letter N printed on it.
Find the probability that this happens when he chooses the 4th card.
Answer(c) ................................................ [3]

Question 4:
Gareth has 8 sweets in a bag.
4 sweets are orange flavoured, 3 are lemon flavoured, and 1 is strawberry flavoured.
(a) He chooses two of the sweets at random.
Find the probability that the two sweets have different flavours.
Answer(a) ................................................ [4]
(b) Gareth now chooses a third sweet.
Find the probability that none of the three sweets is lemon flavoured.
Answer(b) ................................................ [2]

Question 5:

(a) One of these 7 cards is chosen at random.
Write down the probability that the card:
(i) shows the letter A,
Answer(a)(i) ................................................. [1]
(ii) shows the letter A or B,
Answer(a)(ii) ................................................. [1]
(iii) does not show the letter B.
Answer(a)(iii) ................................................. [1]
(b) Two of the cards are chosen at random, without replacement.
Find the probability that:
(i) both show the letter A,
Answer(b)(i) ................................................. [2]
(ii) the two letters are different.
Answer(b)(ii) ................................................. [3]
(c) Three of the cards are chosen at random, without replacement.
Find the probability that the cards do not show the letter C.
Answer(c) ................................................. [2]

Question 6:
Kiah plays a game.
The game involves throwing a coin onto a circular board.
Points are scored based on where the coin lands on the board:

If the coin lands on part of a line or misses the board, then 0 points are scored.

The table below shows the probabilities of Kiah scoring points on the board with one throw:

Points scored	20	10	5	0
Probability	x	0.2	0.3	0.45

(a) Find the value of x.
Answer(a): ................................................. [2]

(b) Kiah throws a coin fifty times.
Work out the expected number of times she scores 5 points.
Answer(b): ................................................. [1]

(c) Kiah throws a coin two times.
Calculate the probability that:
(i) She scores either 5 or 0 with her first throw.
Answer(c)(i): ................................................. [2]
(ii) She scores 0 with her first throw and 5 with her second throw.
Answer(c)(ii): ................................................. [2]
(iii) She scores a total of 15 points with her two throws.
Answer(c)(iii): ................................................. [3]

(d) Kiah throws a coin three times.
Calculate the probability that she scores a total of 10 points with her three throws.
Answer(d): ................................................. [5]

Question 7:
Coins are put into a machine to pay for parking cars.
The probability that the machine rejects a coin is 0.05.

(a) Adhira puts 2 coins into the machine.
(i) Calculate the probability that the machine rejects both coins.
Answer(a)(i): ................................................... [2]

(ii) Calculate the probability that the machine accepts at least one coin.
Answer(a)(ii): ................................................... [1]

(b) Raj puts 4 coins into the machine.
Calculate the probability that the machine rejects exactly one coin.
Answer(b): ................................................... [3]

Question 8:
(a) Haroon has 15 parcels to post.
The table shows information about the sizes of these parcels:

Size	Small	Large
Frequency	9	6

Two parcels are selected at random.
Find the probability that:
(i) both parcels are large.
Answer(a)(i): ................................................... [2]

(ii) one parcel is small and the other is large.
Answer(a)(ii): ................................................... [3]

(b) The probability that a parcel arrives late is 0.08.
4000 parcels are posted.
Calculate an estimate of the number of parcels expected to arrive late.
Answer(b): ................................................... [1]

Question 9:
Prettie picks a card at random from the 11 cards above and does not replace it.
She then picks a second card at random and does not replace it.


(a) Find the probability that she picks:
(i) the letter L and then the letter G.
Answer(a)(i): ................................................... [2]
(ii) the letter E twice.
Answer(a)(ii): ................................................... [2]
(iii) two letters that are the same.
Answer(a)(iii): ................................................... [2]

(b) Prettie now picks a third card at random.
Find the probability that the three letters:
(i) are all the same.
Answer(b)(i): ................................................... [2]
(ii) do not include a letter E.
Answer(b)(ii): ................................................... [2]
(iii) include exactly two letters that are the same.
Answer(b)(iii): ................................................... [5]

Question 10:


Sandra has a fair eight-sided spinner.
The numbers on the spinner are 3, 4, 4, 4, 5, 5, 6, and 8.
Sandra spins the spinner twice and records each number it lands on.

The numbers on the spinner are: 3, 4, 4, 4, 5, 5, 6, 8.

(a) Find the probability that both numbers are 8.
Answer(a): ................................................... [2]

(b) Find the probability that the two numbers are not both 8.
Answer(b): ................................................... [1]

(c) Find the probability that one number is odd and one number is even.
Answer(c): ................................................... [2]

(d) Find the probability that the total of the two numbers is at least 13.
Answer(d): ................................................... [3]

(e) Find the probability that the second number is bigger than the first number.
Answer(e): ................................................... [3]

Question 11:


The diagram shows two fair dice.
The numbers on dice A are 0, 0, 1, 1, 1, 3.
The numbers on dice B are 1, 1, 2, 2, 2, 3.
When a dice is rolled, the score is the number on the top face.

(a) Dice A is rolled once.
Find the probability that the score is not 3.
Answer(a): ................................................. [1]

(b) Dice A is rolled twice.
Find the probability that the score is 0 both times.
Answer(b): ................................................. [2]

(c) Dice A is rolled 60 times.
Calculate an estimate of the number of times the score is 0.
Answer(c): ................................................. [1]

(d) Dice A and dice B are each rolled once.
The product of the scores is recorded.

(i) Complete the possibility diagram.

Answer(d)(i): ................................................. [2]

(ii) Find the probability that the product of the scores is:
(a) 2,
Answer(d)(ii)(a): ................................................. [1]
(b) greater than 3.
Answer(d)(ii)(b): ................................................. [1]

(e) Eva keeps rolling dice B until 1 is scored.
Find the probability that this happens on the 5th roll.
Answer(e): ................................................. [2]