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Either paper 1 mark
A fair six-sided dice is rolled.
Choose the word from this list that best describes the probability that the score is less than 7.
impossible, unlikely, even chance, likely, certain
Show answer
certainA fair dice has six equally likely scores: 1, 2, 3, 4, 5 and 6.
The score is less than 7 for all six of them, so the event is certain.
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Either paper 1 mark
A bag contains 30 counters. 15 of the counters are blue.
One counter is taken from the bag at random.
Which point on the probability scale, A, B or C, shows the probability that the counter is blue?
Show answer
C15 of the 30 counters are blue, so the probability is
\(\frac{ 15 }{ 30 } = \frac{ 1 }{ 2 } = 0.5\)
On the probability scale 0.5 is at point C.
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Either paper 2 marks
The probability that a light bulb made at a factory lasts more than 1000 hours is shown by the point marked A on the probability scale.
(a)Write down this probability as a decimal.
(b)Choose the word that best describes this probability: unlikely, even chance or likely.
Show answer
(a) \(0.5\)
(b) even chanceThe scale runs from 0 to 1 and each small step is 0.1.
Point A is 5 steps along from 0, so the probability is 0.5.
A probability of 0.5 is an even chance, anything below 0.5 is unlikely and anything above 0.5 is likely.
Here the probability is 0.5, so the event is even chance.
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Either paper 3 marks
A bag holds \(14\) counters. Each counter is pink, grey or brown.
\(8\) of the counters are pink, \(1\) are grey and \(5\) are brown.
One counter is taken from the bag at random.
(a)Write down the colour the counter is most likely to be.
(b)Write down the colour the counter is least likely to be.
(c)Choose the word from this list that best describes the probability that the counter is pink.
unlikely, even chance, likely
Show answer
(a) Pink
(b) Grey
(c) likelyEvery counter is equally likely to be taken, so the colour there is most of is the one most likely to come out.
There are \(8\) pink counters, more than of either other colour.
The same reasoning the other way round: \(1\) grey counters is fewer than of either other colour.
Half of \(14\) is \(7\), so a colour with \(7\) counters would be an even chance.
There are \(8\) pink counters, so the probability that the counter is pink is likely.
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Either paper 3 marks
A bag contains 9 counters that are purple and 3 counters that are orange.
One counter is taken at random.
Idris says the probability that it is purple is \(\frac{ 9 }{ 3 }\).
(a)Explain how you can tell that Idris must be wrong, without working the probability out.
(b)Work out the correct probability, giving your answer as a fraction in its simplest form.
Show answer
(a) \(\frac{ 9 }{ 3 }\) is bigger than 1, and no probability can be more than 1.
(b) \(\frac{ 3 }{ 4 }\)\(9\) is bigger than \(3\), so \(\frac{ 9 }{ 3 }\) is greater than 1.
A probability is never more than 1, because an outcome cannot be more than certain.
The bottom of the fraction is the total number of counters, not the number that are orange.
\(9 + 3 = 12\) counters altogether, so the probability is \(\frac{ 9 }{ 12 }\), which is \(\frac{ 3 }{ 4 }\) in its simplest form.
- (b) M1total \(12\) as the denominator, \(\frac{ 9 }{ 12 }\)
- (b) A1simplest form \(\frac{ 3 }{ 4 }\)
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Either paper 4 marks
A fair spinner has five sections, labelled A to E. The spinner is spun once.
(a)Complete these statements.
The spinner is most likely to land on section ________
The spinner is equally likely to land on sections ________ and ________
(b)Two different spinners are spun. One spinner has sections labelled with letters. The other spinner has sections labelled with numbers.
Here is a list of all the possible outcomes.
P 1, P 2, P 3, Q 1, Q 2, Q 3, R 1, R 2, R 3, S 1, S 2, S 3
Show the possible sections on the two spinners.
Letter spinner: ________
Number spinner: ________
Show answer
(a) Most likely: section D. Equally likely: sections A and B.
(b) Letter spinner: P, Q, R, S. Number spinner: 1, 2, 3.The more of the spinner a section takes up, the more likely the spinner is to land on it.
Section D is the largest, so the spinner is most likely to land on section D.
Sections A and B are the same size and no other two sections match, so the spinner is equally likely to land on sections A and B.
Each outcome is one section from each spinner, so a section appears many times in the list. Write each different one once.
The letters that appear are P, Q, R, S, which makes 4 sections.
The numbers that appear are 1, 2, 3, which makes 3 sections.
Check: \(4 \times 3 = 12\), the number of outcomes in the list.
- (a) B1section D, the largest section
- (a) B1sections A and B, the only two sections the same size
- (b) B1letter spinner sections P, Q, R, S, each used once
- (b) B1number spinner sections 1, 2, 3, each used once
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Either paper 2 marks
A fair ordinary dice is rolled once.
(a)On the probability scale, mark with a cross the probability that the dice lands on a number less than 6.
(b)On the probability scale, mark with a cross the probability that the dice lands on a number greater than 4.
You cannot draw on this page. Draw this on paper, then show the answer and check your drawing against the model.
Show answer
(a) \(\frac{ 5 }{ 6 }\): a cross on the tick 5 divisions along from the 0 end
(b) \(\frac{ 1 }{ 3 }\): a cross on the tick 2 divisions along from the 0 end(a)(b)The numbers less than 6 are 1, 2, 3, 4 and 5, which is 5 of the 6 equally likely outcomes.
So the probability is \(\frac{ 5 }{ 6 }\). Put the cross on the tick 5 divisions along from the 0 end.
The numbers greater than 4 are 5 and 6, which is 2 of the 6 equally likely outcomes.
So the probability is \(\frac{ 1 }{ 3 }\). Put the cross on the tick 2 divisions along from the 0 end.
- (a) B1cross at \(\frac{ 5 }{ 6 }\), on the tick 5 divisions along from the 0 end
- (b) B1cross at \(\frac{ 1 }{ 3 }\), on the tick 2 divisions along from the 0 end
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Either paper 2 marks
The table gives the probability of each of four events.
Event A B C D Probability \(0.6\) \(40\%\) \(\frac{1}{20}\) \(0.15\) Write the four events in order of likelihood, starting with the least likely.
Show answer
C, D, B, AWrite every probability in the same form. As decimals:
\(A = 0.6, \qquad B = 0.4, \qquad C = 0.05, \qquad D = 0.15\)
Now put them in order, smallest first:
C, D, B, A
- M1probabilities written in the same form, \(0.6\), \(0.4\), \(0.05\), \(0.15\)
- A1correct order, least likely first: C, D, B, A
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Either paper 2 marks(a)
The probability that a machine breaks down in a day is \(0.5\).
Calculate the probability that the machine does not break down.
(b)Describe in words how likely it is that the machine does not break down.
Show answer
(a) \(0.5\)
(b) an even chanceThe two probabilities add to 1, because either it happens or it does not.
\(1 - 0.5 = 0.5\)
\(0.5\) sits at that end of the probability scale, so it is an even chance.
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Either paper 2 marks
The first bag contains 12 counters. 3 of them are orange.
The second bag contains 18 counters. 6 of them are orange.
One counter is taken at random from each bag.
Which bag gives the better chance of taking a counter that is orange?
You must show your working.
Show answer
the second bag, because \(\frac{ 12 }{36}\) is bigger than \(\frac{ 9 }{36}\)Write both probabilities with the same denominator. Both 12 and 18 divide into 36.
\(\frac{ 3 }{12} = \frac{ 9 }{36}\) and \(\frac{ 6 }{18} = \frac{ 12 }{36}\)
\(\frac{ 12 }{36}\) is the larger, so the second bag gives the better chance.
- M1writes both probabilities over 36, \(\frac{ 12 }{36}\) and \(\frac{ 9 }{36}\)
- A1the second bag