CAIE A-Level Mathematics AS 5.3.3 Exclusive and Independent Events Questions

Practise testing whether events are independent using probability relationships and data.

Exam points

test independence using products of probabilities
use frequency tables and event data to justify independence decisions
calculate intersections when events are independent

[Maximum number: 4]

Jasmine throws two ordinary fair 6-sided dice at the same time and notes the numbers on the uppermost faces. The events A and B are defined as follows.
A : The sum of the two numbers is less than 6 .
$B: \quad$ The difference between the two numbers is at most 2 .

Determine whether or not the events A and B are independent.

$P(A)=\frac{10}{36},\qquad P(B)=\frac{24}{36},\qquad P(A\cap B)=\frac8{36}.$
But
$P(A)P(B)=\frac{10}{36}\frac{24}{36}=\frac5{27}\ne\frac8{36}.$
Therefore, events A and B are not independent.

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CAIE A-Level Mathematics AS 5.3.3 Exclusive and Independent Events Questions question 1