There are 400 students at a school in a certain country. Each student was asked whether they preferred swimming, cycling or running and the results are given in the following table. A student is chosen at random. Determine whether the events 'the student is male' and 'the student prefers swimming' are independent, justifying your answer.  ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_52 Year：2021 Question No：7(a)(ii)

Answer:

Method 1
\( \begin{array}{l} \mathrm{P}(M)=\frac{180}{400}, 0.45 \mathrm{P}(S)=\frac{135}{400}, 0.3375 \mathrm{P}(M \cap S)=\frac{31}{400}, 0.0775 \\ \frac{180}{400} \times \frac{135}{400}=\frac{243}{1600}, 0.151875 \neq \frac{31}{400} \text { so NOT independent } \end{array} \)
Method 2
\( \mathrm{P}(M \cap S)=\frac{31}{400} \mathrm{P}(S)=\frac{135}{400} \mathrm{P}(M)=\frac{180}{400} \)

\( \mathrm{P}(M \mid S)=\frac{\frac{31}{\frac{400}{135}}}{400}=\frac{31}{135}, 0.2296 \ldots \neq \frac{180}{400} \)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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