Probability Basics and the Probability Scale - Worksheets, Questions and Revision

15 original exam-style questions - 10 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Statistics

S18 Probability Basics and the Probability Scale

EDEXCEL 1ST0 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Five words are used in statistics to describe how likely an event is to happen: impossible, unlikely, evens, likely, certain.

Match each description below to the correct probability word.
(a)An event that can never happen.(1)
(b)An event that is just as likely to happen as it is not to happen.(1)
(c)An event that will definitely happen.(1)
(d)An event that probably will not happen, although it is possible.(1)
(e)An event that probably will happen, although it is not certain.(1)
(Total for Question 1 is 5 marks)
2
Each sentence below describes a real event. Write down the probability word (impossible, unlikely, evens, likely or certain) that best describes each one.
(a)A fair coin, tossed once, lands on heads.(1)
(b)The sun rises tomorrow morning.(1)
(c)It snows in the Sahara Desert tomorrow.(1)
(d)A person chosen at random in England was born in December.(1)
(e)It rains somewhere in the UK at some point next week.(1)
(Total for Question 2 is 5 marks)
3
The diagram shows a probability scale from 0 to 1. Five points, A to E, are marked on the scale.
A B C D E 0 1
(a)Write down the letter that shows a probability of 0.5.(1)
(b)Write down the letter that shows an event that is certain to happen.(1)
(c)Write down, in words, the likelihood shown by point B.(1)
(d)A probability of 3/4 is to be marked on the scale as point F. Mark point F on the scale with a cross, and label it F.(2)
(Total for Question 3 is 5 marks)
4
An ordinary fair six-sided dice has faces numbered 1 to 6.
(a)Write down the probability of rolling a 7.(1)
(b)Write down the probability of rolling a number less than 7.(1)
(c)A bag contains only blue counters. State, using one of the words impossible, unlikely, evens, likely or certain, the likelihood of picking a red counter from the bag.(1)
(Total for Question 4 is 3 marks)
5
The spinner shown has 5 equal sections, numbered 1 to 5. The spinner is spun once.
1 2 3 4 5
(a)Write down the probability that the spinner lands on 4.(1)
(b)Work out the probability that the spinner lands on an even number.(2)
(c)By first working out the probability that the spinner lands on a multiple of 3, work out the probability that it does not land on a multiple of 3.(2)
(Total for Question 5 is 5 marks)
6
Probabilities can be written as fractions, decimals or percentages.
(a)A probability is given as 1/4. Write this probability as (i) a decimal and (ii) a percentage.(2)
(b)A probability is given as 0.6. Write this probability as (i) a fraction in its simplest form and (ii) a percentage.(2)
(c)A probability is given as 45%. Write this probability as (i) a decimal and (ii) a fraction in its simplest form.(2)
(Total for Question 6 is 6 marks)
7
A fair coin, which can land on Heads (H) or Tails (T), is tossed once. At the same time, a fair three-sided spinner, with sections numbered 1, 2 and 3, is spun once.
(a)List, systematically, all the possible outcomes of tossing the coin and spinning the spinner together.(2)
(b)Find the probability of getting a Tail and an odd number.(2)
(Total for Question 7 is 4 marks)
8
A bag contains 20 counters. 8 of the counters are red, 5 are blue, and the rest are green. A counter is picked from the bag at random.
(a)Work out the probability that the counter is green.(2)
(b)Work out the probability that the counter is not red.(2)
(Total for Question 8 is 4 marks)
9
For each statement about probability, write down whether it is True or False.
(i)A probability can be written as 1.5.(1)
(ii)The probabilities of all the possible outcomes of an event must add up to 1.(1)
(iii)If a spinner has a probability of 0.5 of landing on blue, it is guaranteed to land on blue exactly 5 times out of 10 spins.(1)
(iv)A probability of 0 means that an outcome is impossible.(1)
(Total for Question 9 is 4 marks)
10
A four-colour spinner is spun once. The table shows some of the probabilities of it landing on each colour.
ColourRedBlueGreenYellow
Probability0.350.250.15?
(a)Work out the probability that the spinner lands on yellow.(2)
(b)Write the probability that the spinner lands on yellow as a percentage.(1)
(c)Using one of the words impossible, unlikely, evens, likely or certain, describe the likelihood that the spinner lands on green.(1)
(Total for Question 10 is 4 marks)
11
A student wants to test whether a six-sided dice is fair, by rolling it many times and recording her results.
(a)State the stage of the statistical enquiry cycle at which the student decides how many times to roll the dice.(1)
(b)State the stage of the statistical enquiry cycle at which the student records the result of each roll.(1)
(c)The student rolls the dice 300 times and a six occurs 74 times. State the stage of the statistical enquiry cycle at which she would calculate the relative frequency of rolling a six, and calculate this relative frequency, giving your answer to 3 significant figures.(3)
(d)The theoretical probability of rolling a six on a fair dice is 1/6 (which is about 0.167 to 3 s.f.). Using this and your answer to part (c), state the stage of the statistical enquiry cycle at which the student would draw a conclusion, and comment on whether her results suggest the dice may be biased.(2)
(Total for Question 11 is 7 marks)
12
A game uses a bag of 50 balls, of which 8 are gold. A ball is picked at random, its colour is noted, and it is then replaced. This is repeated 200 times.
(a)Work out the probability that a single pick gives a gold ball. Give your fraction in its simplest form.(2)
(b)Work out an estimate for the number of times a gold ball would be picked in the 200 picks.(2)
(Total for Question 12 is 4 marks)
13
A bag contains only red counters and blue counters. The probability of picking a red counter at random from the bag is 3/8. There are 24 counters in the bag in total.
(a)Work out the number of red counters in the bag.(2)
(b)Work out the number of blue counters in the bag.(2)
(c)Write the probability of picking a blue counter as a percentage.(2)
(Total for Question 13 is 6 marks)
14
A weather forecaster says: "There is a 70% chance of rain tomorrow." A student says: "This means it will definitely rain for exactly 70% of tomorrow."
(a)Evaluate the student's statement, explaining what a 70% probability of rain actually means.(2)
(b)Using probability vocabulary, state how likely it is to rain tomorrow.(1)
(Total for Question 14 is 3 marks)
15
A charity raffle sells 500 tickets. The probability that a randomly selected ticket is a winning ticket is 0.04.
(a)Work out how many of the 500 tickets are winning tickets.(2)
(b)Sam buys 15 raffle tickets. Explain why 15 x 0.04 = 0.6 cannot simply be used as the probability that at least one of Sam's tickets is a winning ticket.(2)
(Total for Question 15 is 4 marks)
Mark scheme · S18 Probability Basics and the Probability Scale

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15