Question

The probability that a student buys a colouring book is 0.7, and a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find:
(i) The probability that she buys both the colouring book and the box of colours.
(ii) The probability that she buys a box of colours given she buys the colouring book.

Hint:

Use the definition of conditional probability: \( P(A|B) = \frac{P(A \cap B)}{P(B)} \) to switch between joint and conditional probabilities.

Answer 1

Let: \( P(C) = \) Probability of buying a colouring book = 0.7
\( P(B) = \) Probability of buying a box of colours = 0.2
\( P(C|B) = \) Probability of buying colouring book given she buys box = 0.3
(i) By definition of conditional probability: \[ P(C|B) = \frac{P(C \cap B)}{P(B)} \Rightarrow P(C \cap B) = P(C|B) \cdot P(B) = 0.3 \cdot 0.2 = 0.06 \] (ii) Using conditional probability: \[ P(B|C) = \frac{P(C \cap B)}{P(C)} = \frac{0.06}{0.7} = \frac{6}{70} = \frac{3}{35} \approx 0.0857 \]