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P9Conditional probability

Edexcel GCSE Maths (1MA1), Higher tier · Probability

Practise Conditional probability. 2 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy4 marks
Some students were asked how they usually travel to school: walk, bus or car.
The two-way table shows information about their choices.
[object Object]
(a) One of these students is chosen at random.
Work out the probability that this student travels to school by bus.[2]
(b) One of the boys is chosen at random.
Work out the probability that this student walks to school.[2]
Show the answer and mark scheme
(a) Answer: \(\frac{28}{107}\)
  • M1 for a fraction with numerator 28 or with denominator 107
  • A1 for \(\frac{28}{107}\) oe

Worked solution: \(\frac{28}{107}\)

(b) Answer: \(\frac{24}{61}\)
  • M1 for a fraction with numerator 24 or with denominator 61
  • A1 for \(\frac{24}{61}\) oe

Worked solution: There are 61 boys and 24 of them walk to school, so the probability is \(\frac{24}{61}\).

Question 2Medium5 marks
Some students were asked how they usually travel to school: walk, bus or car.
The two-way table shows some information about their choices.
[object Object]
(a) Complete the two-way table.[3]
(b) One of the students who walk to school is chosen at random.
Work out the probability that this student is a girl.[2]
Show the answer and mark scheme
(a) Answer: Boys: 11, 16, 7 (total 34); Girls: 15, 22, 19 (total 56); column totals 26, 38, 26
  • B3 for a fully correct table

Worked solution: Girls total \(90 - 34 = 56\); Girls, Walk \(26 - 11 = 15\); Boys, Bus \(38 - 22 = 16\); Boys, Car \(34 - 11 - 16 = 7\); Car total \(90 - 26 - 38 = 26\); Girls, Car \(26 - 7 = 19\).

(b) Answer: \(\frac{15}{26}\)
  • M1 for a fraction with numerator 15 or with denominator 26 (ft their table)
  • A1 for \(\frac{15}{26}\) oe

Worked solution: 15 of the 26 students who walk to school are girls, so the probability is \(\frac{15}{26}\).

Question 3Hard4 marks
A gym records whether each of its 200 members usually visits in the morning or in the evening, and whether they attend a fitness class.
[object Object]
(a) A member who visits in the evening is chosen at random.
Find the probability that this member attends a class.[1]
(b) The manager says, 'Members who visit in the evening are more likely to attend a class than members who visit in the morning, because 42 is more than 18.'
Is the manager correct? You must show your working.[3]
Show the answer and mark scheme
(a) Answer: \(\frac{42}{140} = \frac{3}{10}\)
  • B1 for \(\frac{42}{140}\) oe

Worked solution: 42 of the 140 evening members attend a class: \(\frac{42}{140} = \frac{3}{10}\).

(b) Answer: No: \(\frac{18}{60} = 0.3\) and \(\frac{42}{140} = 0.3\), so both groups are equally likely to attend a class.
  • M1 for P(class | morning) \(= \frac{18}{60}\)
  • A1 for 0.3 for both groups
  • C1 for 'no' with the explanation that the proportions are equal (there are more evening members, so comparing 42 with 18 is not fair)

Worked solution: Morning: \(\frac{18}{60} = 0.3\). Evening: \(\frac{42}{140} = 0.3\).
The probabilities are the same. There are more evening members, which is why 42 > 18. The manager is not correct.

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