Oxford AQA International A-level · Mathematics (9660)

Further probability: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Further probability.

10 questions29 marksFree, no account

Question 1

1 mark

For two events \(A\) and \(B\), it is given that \(P(A) = 0.3\), \(P(B) = 0.5\), and \(P(A | B) = 0.4\). Calculate the conditional probability \(P(B | A)\).

Question 2

1 mark

The conditional probabilities for event \(A\) given event \(B\) and its complement \(B'\) are \(P(A | B) = 0.7\) and \(P(A | B') = 0.4\). If \(P(B) = 0.3\), calculate the value of \(P(B | A)\).

Question 3

1 mark

Two events \(A\) and \(B\) are mutually exclusive. Given that \(P(A) = 0.25\) and \(P(B) = 0.45\), find the value of \(P(A' \cap B')\).

Question 4

1 mark

For two events \(A\) and \(B\), it is given that \(P(A | B) = 0.5\), \(P(B | A) = 0.4\), and \(P(A \cap B) = 0.2\). Calculate \(P(A' \cap B')\).

Question 5

1 mark

Events \(A\) and \(B\) are independent such that \(P(A) = 0.6\) and \(P(B) = 0.5\). Calculate \(P(A \cup B)\).

Question 6

3 marks

Events \(A\) and \(B\) are independent such that \(P(A) = 0.4\) and \(P(A \cup B) = 0.7\). Calculate the probability \(P(B)\).

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Question 7

6 marks

Given that \(P(A) = 0.6\), \(P(B) = 0.5\), and \(P(A | B) = 0.8\), find the conditional probability \(P(B | A')\).

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Question 8

5 marks

Three events \(A\), \(B\), and \(C\) are defined. Events \(A\) and \(B\) are mutually exclusive with \(P(A) = 0.3\) and \(P(B) = 0.4\). If event \(C\) is independent of the event \((A \cup B)\) and \(P(C) = 0.5\), find \(P((A \cup B) \cap C)\).

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Question 9

4 marks

For two events \(A\) and \(B\), it is given that \(P(A) = 0.35\), \(P(B) = 0.45\), and \(P(A \cup B) = 0.6\).

(a) Calculate \(P(A \cap B)\).
(b) Find the conditional probability \(P(A | B)\).
(c) Determine, with a reason, whether events \(A\) and \(B\) are independent.

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Question 10

6 marks

In a factory, machine A produces 60% of the total output and machine B produces the remaining 40%. The probability of a defective component being produced by machine A is 0.02, while the probability for machine B is 0.05.

(a) A component is selected at random from the total output. Find the probability that it is defective.
(b) Given that a randomly selected component is found to be defective, find the probability that it was produced by machine A.
(c) Two components are selected at random. Find the probability that exactly one is defective.

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