Robinson Tuition
Grade 9 · Higher · free GCSE maths worksheet

Probability with algebra

Unknown probabilities leading to equations.

12 original questions, 52 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A bag contains 2x green counters and (x + 4) yellow counters. A counter is taken at random.

The probability that it is green is 25.

Work out the value of x.

3 marks
Show answer
x = 2
2

A bag contains n counters. 3 of the counters are red.

A counter is taken at random, replaced, and then a second counter is taken at random.

Write down an expression, in terms of n, for the probability that both counters are red.

2 marks
Show answer
9n2
3

A box contains n counters. 5 of the counters are green.

A counter is taken at random and not replaced. A second counter is then taken at random.

Write down an expression, in terms of n, for the probability that both counters are green.

2 marks
Show answer
20n(n-1)
4

A biased coin is flipped twice. The flips are independent.

The probability of getting heads on both flips is 0.64.

Work out the probability of getting heads on one flip of the coin.

2 marks
Show answer
0.8
5

50 people were asked whether they read fiction (A) or non-fiction (B).

The Venn diagram regions contain these numbers of people:

A only: x   A ∩ B: 5   B only: 2x − 3   neither: x + 8

  1. Work out the value of x.
  2. One of the 50 people is chosen at random. Work out the probability that this person reads non-fiction.
ξABx52x − 3x + 8
4 marks
Show answer
a) 10 b) 11/25
6

Two independent events A and B are such that

P(B) = 2 × P(A)

P(A and B) = 18

Find P(A).

4 marks
Show answer
14
7

A jar contains n sweets. 6 of the sweets are orange. The rest are lemon.

Hana takes two sweets at random, without replacement.

The probability that both sweets are orange is 13.

  1. Show that n² − n − 90 = 0.
  2. Find the value of n.
5 marks
Show answer
a) P(both orange) = 6/n × 5/(n-1) = 30/(n(n-1)) = 1/3, so n(n-1) = 90, giving n² - n - 90 = 0 b) 10
8

A bag contains x green counters and 8 white counters.

Two counters are taken at random, without replacement.

The probability that both counters are white is 1433.

Work out the value of x.

5 marks
Show answer
4
9

A bag contains only red counters and green counters.

The probability of taking a red counter at random is 25.

10 red counters are then removed from the bag.

The probability of taking a red counter at random is now 14.

Work out the number of counters that were in the bag originally.

5 marks
Show answer
50
10

A bag contains 4 red counters and x blue counters. Two counters are taken at random without replacement.

  1. Show that the probability of taking one red counter and one blue counter is 8x(x + 4)(x + 3).
  2. The probability of taking one counter of each colour is 815. Show that x2 − 8x + 12 = 0.
  3. Solve x2 − 8x + 12 = 0 to find the possible values of x.
6 marks
Show answer
a) shown b) shown c) x = 2 or x = 6
11

A bag contains x black counters and 6 white counters.

Two counters are taken at random, without replacement.

The probability that the two counters are different colours is 12.

Find the possible values of x.

6 marks
Show answer
x = 3 or x = 10
12

There are n counters in a box. 8 of the counters are orange. The rest are brown.

Meg takes two counters at random, without replacement.

The probability that both counters are orange is 415.

  1. Show that n² − n − 210 = 0.
  2. Find the value of n.
  3. Work out the probability that both counters Meg takes are brown.
8 marks
Show answer
a) P(both orange) = 8/n × 7/(n-1) = 56/(n(n-1)) = 4/15, so n(n-1) = 210, giving n² - n - 210 = 0 b) 15 c) 1/5

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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