CAIE A-Level Mathematics AS 5.3.2 Probability Rules Questions

Practise calculating conditional, joint and complementary probabilities for dependent events.

Exam points

calculate conditional probabilities from event information
use tree diagrams and set relationships for dependent events
solve multi-stage probability problems with joint and complementary events

[Maximum number: 3]

Box A contains 6 green balls and 3 yellow balls.
Box B contains 4 green balls and x yellow balls.
A ball is chosen at random from box A and placed in box B. A ball is then chosen at random from box B.

The probability that both the balls chosen are the same colour is $\frac{8}{15}$ .

Find the value of x.

The probability of choosing two balls of the same colour is
$\frac69\left(\frac5{5+x}\right)+\frac39\left(\frac{1+x}{5+x}\right)=\frac8{15}.$
Rearranging,
15(x+11)=24(x+5),
so
x=5.

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CAIE A-Level Mathematics AS 5.3.2 Probability Rules Questions question 1