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 events $E$ and $F$ are such that

$\mathrm{P}(E) = x \qquad \mathrm{P}(F) = y \qquad \mathrm{P}(E \mid F) = 0.25 \qquad \mathrm{P}(E' \cap F') = 0.3$
(a) Show that $20x + 15y = 14$

(3 marks)

A third event $G$ is mutually exclusive with $E$ . Also

$\mathrm{P}(G) = y - 0.3 \qquad \mathrm{P}(E \cup G) = 0.55$
(b) (i) Form a second equation in $x$ and $y$

(ii) Hence find the values of $x$ and $y$

(4 marks)
(c) Determine whether or not the events $E$ and $F$ are statistically independent. You must show your working clearly.

(2 marks)
Level 4 · 9 marksTry it