A-level · Probability

Mutually exclusive and independent eventsExam-style questions

The two key relationships between events: mutually exclusive (they cannot both happen, so P(A∩B) = 0 and P(A∪B) = P(A) + P(B)) and independent (one does not affect the other, so P(A∩B) = P(A)×P(B)). How to use each rule, how to TEST whether two events are independent, and why mutually exclusive and independent are not the same thing.

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9 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
The mutually exclusive events $A$ and $B$ have $P(A) = 0.3$ and $P(B) = 0.4$ . Find $P(A \cup B)$ .
Level 2 · 2 marksTry it
2
The probabilities of the regions formed by two events, $A$ and $B$ , are given in the Venn diagram below. The values of $p$ and $q$ are unknown.The events $A$ and $B$ are independent.
(a) Find the value of $p$ and the value of $q$

(3 marks)
(b) Find $\mathrm{P}(A' \mid B)$

(2 marks)
Level 2 · 5 marksTry it
3
Two events $J$ and $K$ are such that

$\mathrm{P}(J \cup K) = 0.71 \qquad \mathrm{P}(K) = 0.45 \qquad \mathrm{P}(J \mid K) = 0.36$
(a) Find $\mathrm{P}(J \cap K)$

(2 marks)
(b) Find $\mathrm{P}(J)$

(2 marks)

For two further events $L$ and $M$ ,

$\mathrm{P}(L) = x^2 \qquad \mathrm{P}(M) = 1.3 - x$

where $x$ is a constant and $0.3 \leqslant x \leqslant 1$
(c) Show that it is not possible for $L$ and $M$ to be mutually exclusive.

(4 marks)
Level 3 · 8 marksTry it
4
The independent events $A$ and $B$ have $P(A) = 0.5$ and $P(B) = 0.4$ . Find $P(A \cap B)$ .
Level 3 · 2 marksTry it
5
For events $A$ and $B$ , $P(A) = 0.6$ , $P(B) = 0.3$ and $P(A \cap B) = 0.18$ . Determine whether $A$ and $B$ are independent.
Level 3 · 2 marksTry it

4 more questions on mutually exclusive and independent events

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