Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 10
108 practice questions
Topics covered
Practice questions
81–90 of 108
Question 81
2 marks · Normal
Answer and see the solution →A bag contains 4 red marbles and 6 blue marbles. A marble is taken at random, replaced, and then another marble is taken at random.
Work out the probability that both marbles are blue.
Question 82
3 marks · Normal
Answer and see the solution →A bag contains 3 green counters and 2 yellow counters. Two counters are taken from the bag one after the other, without replacement.
Draw a tree diagram to show all the possible outcomes. Use your diagram to calculate the probability that both counters are green.
Question 83
3 marks · Normal
Answer and see the solution →A box contains some balls. The probability that a randomly chosen ball is black is 0.2, and the probability that it is white is 0.5. The probability that it is red is unknown.
Given that the ball chosen is not black, explain how you would calculate the probability that it is white.
Question 84
4 marks · Normal
Answer and see the solution →You roll a fair six-sided die twice.
(a)[1 mark]Write down the probability of getting a 2 on the first roll and a 4 on the second roll.
(b)[2 marks]Find the probability of getting an even number on both rolls.
(c)[1 mark]Calculate the probability of getting at least one 6 in the two rolls.
Question 85
2 marks · Normal
Answer and check →A coin is biased so that the probability of getting a tail is 0.55.
Given that the coin has landed on a tail, what is the probability it will land on a tail again in the next flip? (The two flips are independent.)
Question 86
3 marks · Normal
Answer and see the solution →A box contains 5 pens: 3 blue and 2 black. Two pens are taken at random, one after the other, without replacement.
Work out the probability that both pens are black.
Question 87
4 marks · Normal
Answer and see the solution →The probability that a machine produces a defective part is 0.1. The probability that a randomly chosen part was produced by machine A is 0.6, and by machine B is 0.4. The events are independent.
A part is selected at random. The possible outcomes are that the part was produced by machine A or B, and that the part is defective or not defective.
Construct a tree diagram to show all possible outcomes and their probabilities. Complete the probability table below.
Complete the missing probabilities in the table. Write all probabilities as decimals. Produced by Defective? Probability A Yes A No B Yes B No Question 88
3 marks · Normal
Answer and see the solution →A spinner can land on red, blue, or green. The probability of red is 0.3, the probability of blue is 0.4, and the probability of green is 0.3. Two independent spins are made.
Explain, with reference to a tree diagram, why the sum of the probabilities of all the possible outcomes is equal to 1.
Question 89
2 marks · Hard
Answer and see the solution →A bag contains 5 red counters and 3 blue counters. Two counters are taken from the bag one after the other, without replacement. What is the probability that both counters are red? Give your answer as a fraction in its simplest form.
Question 90
4 marks · Hard
Answer and see the solution →A company has two machines, A and B, producing light bulbs. - Machine A produces 60% of the bulbs, and machine B produces 40%. - 3% of the bulbs produced by machine A are defective. - 5% of the bulbs produced by machine B are defective. A bulb is selected at random. Draw a tree diagram showing all possible outcomes and use it to calculate the probability that a randomly chosen bulb is defective.