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.

▶️Answer/Explanation

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.

▶️Answer/Explanation

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.

Scroll to Top