Conditional Probability
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Either paper 4 marks
A bag contains 5 green cubes and 3 white cubes.
Two cubes are taken from the bag at random, one after the other. The first cube is not put back before the second one is taken.
The tree diagram is not complete.
(a)State the probability that the second cube is green, given that the first cube is green.
(b)Work out the probability that both cubes are green.
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Either paper 3 marks
The Venn diagram shows information about a group of 30 students.
Circle Instrument shows the students who play a musical instrument. Circle Choir shows the students who are in the school choir.
(a)One of the students is chosen at random.
Given that this person is one of those who play a musical instrument, find the probability that this person is also one of those who are in the school choir.
(b)Given instead that this person is one of those who are in the school choir, find the probability that this person is also one of those who play a musical instrument.
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Either paper 4 marks
A year group has 61 students.
21 of the students have a part-time job.
\(\frac{ 2 }{ 3 }\) of the students who have a part-time job play football.
Of the students who do not have a part-time job, 40% play football.
The Venn diagram shows the sets Job and Football.
(a)Complete the Venn diagram.
(b)One of the students who play football is chosen at random.
Work out the probability that this student has a part-time job.
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Either paper 3 marks
A bag contains 4 red counters and 3 blue counters.
Two counters are taken from the bag at random, one after the other, without replacement.
Find the probability that the two counters are the same colour.
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Either paper 4 marks
A bag contains 7 toffee sweets and 4 mint sweets.
Two sweets are taken from the bag at random, one after the other, without replacement.
Work out the probability that the two sweets are different flavours.
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Either paper 6 marks
On any morning Callum walks to school.
The probability that it rains is \(\frac{ 5 }{ 6 }\).
If it rains, the probability that Callum is late is \(\frac{ 3 }{ 7 }\).
If it does not rain, the probability that Callum is late is \(\frac{ 1 }{ 7 }\).
(a)State the probability that Callum is late, given that it rains.
(b)Find the probability that it rains and Callum is late.
(c)Find the probability that Callum is late.
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Either paper 3 marks
A bag contains 2 toffee sweets, 7 mint sweets and 5 fruit sweets.
Anya takes two sweets at random from the bag, without replacement.
Calculate the probability that she takes sweets of different flavours.
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Either paper 4 marks
A bag contains 4 red cubes and 6 yellow cubes.
Three cubes are taken from the bag at random, one after the other, without replacement.
Find the probability that all three cubes are red.
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Either paper 4 marks
A bag contains 3 winning tickets and 5 blank tickets.
Two tickets are taken from the bag at random, one after the other, without replacement.
Calculate the probability that at least one of the two tickets is winning.
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Either paper 3 marks
A bag contains 30 discs. 8 are yellow, 11 are purple and 11 are white.
Dev takes three of the discs at random without replacement. Dev's first disc is white.
Calculate the probability that all three discs are different colours.
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(a) \(\frac{4}{7}\)
(b) \(\frac{5}{14}\) -
(a) \(\frac{3}{16}\)
(b) \(\frac{3}{7}\) -
(a) Job only \(7\); both \(14\); Football only \(16\); neither \(24\)
(b) \(\frac{7}{15}\) - \(\frac{3}{7}\)
- \(\frac{28}{55}\)
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(a) \(\frac{3}{7}\)
(b) \(\frac{5}{14}\)
(c) \(\frac{8}{21}\) - \(\frac{59}{91}\)
- \(\frac{1}{30}\)
- \(\frac{9}{14}\)
- \(\frac{44}{203}\)
Takes a couple of seconds the first time a sheet is made.