# IBDP Maths analysis and approaches Topic: AHL 4.13 Use of Bayes’ theorem for a maximum of three events HL Paper 1

## Question

At a nursing college, 80 % of incoming students are female. College records show that 70 % of the incoming females graduate and 90 % of the incoming males graduate. A student who graduates is selected at random. Find the probability that the student is male, giving your answer as a fraction in its lowest terms.

## Markscheme

$${\text{P }}M|G = \frac{{{\text{P}}(M \cap G)}}{{{\text{P}}(G)}}$$     (M1)

$$= \frac{{0.2 \times 0.9}}{{0.2 \times 0.9 + 0.8 \times 0.7}}$$     M1A1A1

$$= \frac{{0.18}}{{0.74}}$$

$$= \frac{9}{{37}}$$     A1

[5 marks]

## Examiners report

Most candidates answered this question successfully. Some made arithmetic errors.

## Question

Jenny goes to school by bus every day. When it is not raining, the probability that the bus is late is $$\frac{3}{{20}}$$. When it is raining, the probability that the bus is late is $$\frac{7}{{20}}$$. The probability that it rains on a particular day is $$\frac{9}{{20}}$$. On one particular day the bus is late. Find the probability that it is not raining on that day.

## Markscheme

(A1)

$${\text{P}}(R’ \cap L) = \frac{{11}}{{20}} \times \frac{3}{{20}}$$     A1

$${\text{P}}(L) = \frac{9}{{20}} \times \frac{7}{{20}} + \frac{{11}}{{20}} \times \frac{3}{{20}}$$     A1

$${\text{P}}(R’|L) = \frac{{{\text{P}}(R’ \cap L)}}{{{\text{P}}(L)}}$$     (M1)

$$= \frac{{33}}{{96}}{\text{ }}\left( { = \frac{{11}}{{32}}} \right)$$     A1

[5 marks]

## Examiners report

This question was generally well answered with candidates who drew a tree diagram being the most successful.

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