Probability Sum to 1
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Either paper 2 marks
A spinner can land on red, blue, green or yellow.
The table gives the probability of each colour.
Colour Red Blue Green Yellow Probability \(0.35\) \(0.15\) \(0.1\) ? Work out the probability that the spinner lands on yellow.
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Either paper 4 marks
A game is played 60 times. The chart shows the winning score each time.
(a)Write down the mode of the winning scores.
(b)The game is played again. Use the chart to estimate the probability that the winning score is 26.
(c)Use the chart to estimate the probability that the winning score is 24 or more.
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Either paper 3 marks
Here is a fair ordinary dice and a fair spinner. Every section of the spinner is the same size.
In one turn of a game, Anya throws the dice once and spins the spinner once.
Is Anya more likely to get a number less than 2 on the dice or a number greater than 5 on the spinner?
You must show all your working.
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Either paper 3 marks
A bag contains 12 counters. 3 of the counters are black.
One counter is taken from the bag at random.
(a)Work out the probability that the counter is black. Give your answer as a fraction in its simplest form.
(b)Work out the probability that the counter is not black.
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Either paper 3 marks
A bag contains counters. Some are purple and the rest are orange.
The probability that a counter taken at random is purple is \(\frac{ 1 }{ 4 }\).
There are 5 counters that are purple.
(a)Calculate how many counters there are altogether.
(b)Calculate how many counters are orange.
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Either paper 3 marksA spinner can land on yellow, green or red only. Priya writes down these probabilities.
Colour Probability yellow 0.3 green 0.4 red 0.4 (a)Explain how you can tell that Priya has made a mistake.
(b)By how much is the total of Priya's probabilities wrong?
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Either paper 2 marks
A bag contains counters that are yellow, green, red or blue.
One counter is taken at random.
The probability that it is yellow is \(0.3\).
The probability that it is green is \(0.25\).
(a)Calculate the probability that the counter is yellow or green.
(b)Calculate the probability that the counter is neither yellow nor green.
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Either paper 3 marks
A fair spinner is numbered 1 to 5. It is spun once.
A bag contains counters in three colours: blue, purple and orange.
The table shows the probability of taking each colour, except one.
Colour Blue Purple Orange Probability \(0.35\) \(0.35\) ? (a)Find the probability that a counter taken at random from the bag is orange.
(b)Find the probability that the spinner lands on a number greater than 2.
(c)Decide which is more likely: spinning a number greater than 2 on the spinner, or picking an orange counter from the bag.
Give a reason for your answer.
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Either paper 3 marks
A fair spinner has 12 equal sections.
Label each section A, B, C or D so that when the arrow is spun: the probability it lands on B is \(\frac{ 1 }{ 6 }\); the probability it lands on C is equal to the probability it lands on D; the probability it lands on A is three times the probability it lands on B.
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Either paper 3 marks
A fair, ordinary dice is rolled and a counter is taken at random from a bag.
The tree diagram shows the probabilities.
(a)How do the probabilities show that all the counters in the bag are red, blue or yellow?
(b)Write down the probability that the counter is red or yellow.
(c)Write down the probability that the dice lands on an even number and the counter is red.
- \(0.4\)
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(a) \(24\)
(b) \(\frac{ 7 }{ 60 }\)
(c) \(\frac{ 37 }{ 60 }\) - The dice: dice \(\frac{ 1 }{ 6 } = \frac{ 3 }{ 18 }\), spinner \(\frac{ 1 }{ 9 } = \frac{ 2 }{ 18 }\)
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(a) \(\frac{1}{4}\)
(b) \(\frac{3}{4}\) -
(a) \(20\)
(b) \(15\) -
(a) The three probabilities add to \(1.1\), and the probabilities of all the outcomes must add to exactly 1.
(b) \(0.1\) -
(a) \(0.55\)
(b) \(0.45\) -
(a) \(0.3\)
(b) \(0.6\)
(c) The spinner, because \(0.6\) > \(0.3\) - B: 2, C: 2, D: 2, A: 6 (12 sections in total; any arrangement of the sections is accepted)
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(a) The three probabilities from each counter node add up to 1: \(\frac{ 6 }{ 25 } + \frac{ 12 }{ 25 } + \frac{ 7 }{ 25 } = 1\), so no other colour is possible.
(b) \(\frac{13}{25}\)
(c) \(\frac{3}{25}\)
Takes a couple of seconds the first time a sheet is made.