Combined & Conditional Probability Practice Questions

Question 1

4 marks

On Rosa's walk to work there are two sets of traffic lights.

The probability that the first set of lights is on red when Rosa reaches it is $0.3$

The probability that the second set of lights is on red when Rosa reaches it is $0.45$

The two events are independent.

(a)

Work out the probability that both sets of lights are on red when Rosa reaches them.

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(b)

Work out the probability that neither set of lights is on red when Rosa reaches them.

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Question 2

3 marks

100 students at a school were asked how they usually travel to school.

The two-way table shows information about their answers.

	Year 10	Year 11	Total
Bus	18	14	32
Car	9	16	25
Walk	23	20	43
Total	50	50	100

(a)

One of the 100 students is chosen at random.

Write down the probability that this student usually travels to school by car.

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(b)

One of the Year 11 students is chosen at random.

Write down the probability that this student usually walks to school.

/ 1

(c)

One of the 100 students is chosen at random.

Given that this student usually travels to school by bus, find the probability that the student is in Year 10.

/ 1

Question 0

3 marks

There are 30 students in a class.

17 of the students have a dog.
11 of the students have a cat.

Ravi says,

"If you choose one of the 30 students at random, the probability that the student has a dog or has a cat is $\frac{17}{30}+\frac{11}{30}=\frac{28}{30}$ "

(a)

Explain why Ravi's method may not give the correct probability.

/ 1

(b)

5 of the 30 students have both a dog and a cat.

One of the 30 students is chosen at random.

Work out the probability that this student has a dog or has a cat.

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Question 0

4 marks

A box contains 12 chocolates.
5 of the chocolates are milk chocolates.
7 of the chocolates are dark chocolates.

Jon takes at random two chocolates from the box and eats them.

(a)

Work out the probability that the two chocolates are the same type.

You must show your working.

/ 3

(b)

Before doing any working, Jon said,

"5 out of the 12 chocolates are milk chocolates, so the probability that both chocolates are milk chocolates is $\frac{5}{12}\times\frac{5}{12}$ "

Explain why Jon is wrong.

/ 1

Question 0

5 marks

40 students were asked whether they use Netflix (N) and whether they use Spotify (S).

The Venn diagram shows information about their answers.

(a)

One of the 40 students is chosen at random.

Write down the probability that this student uses neither Netflix nor Spotify.

/ 1

(b)

One of the 40 students is chosen at random.

Given that this student uses Spotify, find the probability that the student also uses Netflix.

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(c)

Two of the 40 students are chosen at random.

Work out the probability that both of these students use neither Netflix nor Spotify.

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Question 0

4 marks

A jar contains 10 marbles.
7 of the marbles are blue and 3 of the marbles are white.

Priya takes at random three marbles from the jar. She does not replace them.

(a)

Work out the probability that all three marbles are blue.

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(b)

Work out the probability that at least one of the three marbles is white.

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Question 0

4 marks

A bag contains only red counters and blue counters.

There are 6 red counters in the bag.

Sam takes at random two counters from the bag. He does not replace them.

The probability that both counters are red is $\frac13$

Work out the number of blue counters in the bag.

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Question 0

5 marks

A company has 180 employees.

The ratio of the number of full-time employees to the number of part-time employees is $7:2$

30% of the full-time employees cycle to work.
75% of the part-time employees cycle to work.

(a)

One of the 180 employees is chosen at random.

Work out the probability that this employee cycles to work.

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(b)

One of the 180 employees is chosen at random.

Given that this employee cycles to work, find the probability that the employee is part-time.

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Question 0

4 marks

A bag contains 12 beads.

3 of the beads are red, 4 of the beads are blue and 5 of the beads are green.

Maya takes at random three beads from the bag.

Work out the probability that she takes one bead of each colour.

You must show your working.

/ 4

Question 0

5 marks

A factory makes one type of switch.

65% of the switches are made on machine A.
The rest of the switches are made on machine B.

3% of the switches made on machine A are faulty.
8% of the switches made on machine B are faulty.

(a)

A switch is chosen at random from all the switches made by the factory.

Work out the probability that this switch is faulty.

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(b)

A switch is chosen at random from all the switches made by the factory.

Given that this switch is faulty, find the probability that it was made on machine B.

/ 2

Number

Algebra

Ratio, Proportion & Rates of Change

Geometry & Measures

Probability

Statistics

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