Pearson Edexcel GCSE (9-1) · Mathematics (1MA1)
5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Conditional probability (Higher).
A bag contains only red, blue, and yellow counters.
The ratio of red counters to blue counters is \(3 : 5\).
The probability of picking a yellow counter is \(0.2\).
If there are 24 blue counters in the bag, calculate the total number of counters in the bag.
A bag contains \(n\) counters, of which 5 are red and the rest are blue.
Two counters are taken at random from the bag without replacement.
The probability that both counters are red is \(\frac{5}{33}\).
Find the total number of counters, \(n\), in the bag.
A bag contains only red, blue, and green marbles.
The probability of picking a red marble is \(0.3\).
The probability of picking a blue marble is \(0.45\).
What is the probability of picking a green marble?
A bag contains 5 red balls and \(y\) blue balls.
Two balls are taken at random without replacement.
The probability that one ball is red and the other is blue is \(\frac{1}{2}\).
Find the possible values of \(y\).
In a group of 100 people, 70 like tea (T), 60 like coffee (C), and 25 like neither.
A person is chosen at random from the group.
Find the probability that this person likes both tea and coffee.
A bag contains only red, blue, and green counters.
The probability of picking a red counter is 0.3.
The probability of picking a blue counter is 0.4.
Find the probability of picking a green counter.
Write your answer out first, then check it against the worked solution.
In a class of 30 students, 18 study Art (\( A \)) and 15 study Biology (\( B \)). 7 students study both subjects.
Given that a student selected at random studies Art, find the probability that they also study Biology.
Write your answer out first, then check it against the worked solution.
A bag contains x red counters and (x + 3) blue counters. Two counters are taken at random from the bag without replacement.
The probability that both counters are the same colour is \(\frac{1}{2}\).
Form an equation in terms of \(x\) and solve it to find the total number of counters in the bag.
Write your answer out first, then check it against the worked solution.
A bag contains \(6\) red counters and \(4\) blue counters. Jane takes at random a counter from the bag and notes its colour. She does not replace the counter. She then takes at random a second counter from the bag.
(a) Calculate the probability that Jane takes two counters of the same colour.
(b) Calculate the probability that Jane takes at least one blue counter.
Write your answer out first, then check it against the worked solution.
A bag contains \( n \) counters. 7 of the counters are green and the rest are blue.
Two counters are taken at random from the bag without replacement.
The probability that both counters are green is \( \frac{7}{15} \).
(a) Show that \( n^2 - n - 90 = 0 \).
(b) Find the value of \( n \) and hence find the number of blue counters in the bag.
Write your answer out first, then check it against the worked solution.
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