Moderate -0.8 This is a straightforward application of Bayes' theorem with clearly stated probabilities and a standard two-stage tree diagram setup. The calculation requires only basic probability rules (multiplication and addition) with no conceptual subtleties, making it easier than average for A-level.
5 In a certain country \(54 \%\) of the population is male. It is known that \(5 \%\) of the males are colour-blind and \(2 \%\) of the females are colour-blind. A person is chosen at random and found to be colour-blind. By drawing a tree diagram, or otherwise, find the probability that this person is male.
**Option 1 (Tree diagram shown):**
| M1 | For correct shape ie M and F first
| A1 | All correct, ie labels and probabilities, no labels gets M1 only for (implied)correct shape
**Option 2 (Calculation):**
$P(M \text{ and } C)$ and $P(F \text{ and } C)$ | M1 | For finding $P(M \text{ and } C)$ and $P(F \text{ and } C)$
| A1 | For using 4 correct probs
$P(M|C) = \frac{0.54 \times 0.05}{0.54 \times 0.05 + 0.46 \times 0.02}$ $= 0.746$ ($\frac{135}{181}$) | M1 | For correct conditional probability
B1 | For correct numerator
M1 | For summing two two-factor 'terms'
A1 | For correct answer
**6 marks total**
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5 In a certain country $54 \%$ of the population is male. It is known that $5 \%$ of the males are colour-blind and $2 \%$ of the females are colour-blind. A person is chosen at random and found to be colour-blind. By drawing a tree diagram, or otherwise, find the probability that this person is male.
\hfill \mbox{\textit{CAIE S1 2003 Q5 [6]}}