A total of 500 students were asked which one of four colleges they attended and whether they preferred soccer or hockey. The numbers of students in each category are shown in the following table. One of the students is chosen at random. Determine whether the events 'the student prefers hockey' and 'the student is at Amos college or Benn college' are independent, justifying your answer. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_52 Year：2020 Question No：2(c)

Answer:

\(\mathrm{P}(\) hockey \()=\frac{220}{500}=0.44\)
\(\mathrm{P}(\) Amos or Benn \()=\frac{242}{500}=0.484\)
\(\mathrm{P}\left(\right.\) hockey \(\cap\) A or B) \(=\frac{104}{500}=0.208\)
\(\mathrm{P}(\mathrm{H}) \times \mathrm{P}(\mathrm{A} U \mathrm{~B})=\mathrm{P}(\mathrm{H} \cap(\mathrm{A} U \mathrm{~B}))\) if independent
\(\frac{220}{500} \times \frac{242}{500}=\frac{1331}{6250}\) so not independent

Knowledge points:

5.3.1 evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events, or by calculation using permutations or combinations (e.g. the total score when two fair dice are thrown.) (e.g. drawing balls at random from a bag containing balls of different colours.)

5.3.3 understand the meaning of exclusive and independent events, including determination of whether events A and B are independent by comparing the values of

Answer:

Knowledge points:

Solution:

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