Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
81–90 of 106
Question 81
3 marks · Normal
Answer and see the solution →A spinner has three equal sectors labelled A, B, and C. The spinner is spun twice. Draw a tree diagram and calculate the probability that:
(a)[1 mark]Both spins result in the letter B.
(b)[2 marks]At least one spin shows the letter C.
Question 82
3 marks · Normal
Answer and see the solution →Two fair coins are tossed. Explain, using probability, whether getting one head and one tail is more likely than getting two heads.
Question 83
4 marks · Normal
Answer and see the solution →A bag contains 3 yellow marbles and 2 green marbles. One marble is picked at random, replaced, and then another is picked. Answer the following:
(a)[1 mark]Write down the probability of picking a yellow marble both times.
(b)[1 mark]Write down the probability of picking a green marble first and a yellow marble second.
(c)[2 marks]Find the probability that the two marbles are of different colours.
Question 84
4 marks · Normal
Answer and see the solution →A machine produces three types of screws: Small (S), Medium (M), and Large (L). The probability that a screw is small is 0.2, medium is 0.5, and large is 0.3.
Complete the tree diagram table below showing the probabilities for producing two screws, one after the other, with replacement.
Probabilities for two screws First screw Second screw Probability S S S M S L M S M M M L L S L M L L Question 85
2 marks · Normal
Answer and see the solution →A fair die is thrown twice. What is the probability of getting at least one six in the two throws?
Question 86
3 marks · Normal
Answer and see the solution →Two cards are selected randomly, with replacement, from a deck of 52 playing cards. What is the probability that both cards are aces?
Question 87
3 marks · Normal
Answer and see the solution →Emma spins a spinner twice, each time with probability 1/4 of landing on red and 3/4 of landing on blue. She draws a tree diagram to represent this. Explain, with reasoning, why the total probability for all possible outcomes is 1.
Question 88
2 marks · Hard
Answer and see the solution →A bag contains 5 blue counters and 3 red counters. Two counters are picked from the bag one after the other, without replacement. What is the probability that both counters picked are red?
Question 89
2 marks · Hard
Answer and see the solution →The table shows the probability that each branch is followed on a probability tree diagram. | First Event | Probability | |:-----------:|:----------:| | Heads | 0.4 | | Tails | 0.6 |
What does the sum of the probabilities on the branches from any single event add up to in a tree diagram? Explain briefly.
Question 90
4 marks · Hard
Answer and see the solution →A box contains 3 orange balls and 2 purple balls. A ball is picked at random, not replaced, then a second ball is picked at random.
Calculate the probability that: (a) Both balls are orange (b) The two balls picked are different colours
(a)[2 marks]Calculate the probability that both balls are orange.
(b)[2 marks]Calculate the probability that the two balls are different colours.