Two ordinary fair dice, one red and the other blue, are thrown. Event $$$A$$$ is 'the score on the red die is divisible by 3 '. Event $$$B$$$ is 'the sum of the two scores is at least 9 '. Hence determine whether or not the events $$$A$$$ and $$$B$$$ are independent. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_51 Year：2020 Question No：1(b)

Answer:

$
\mathrm{P}(\mathrm{A}) \times \mathrm{P}(\mathrm{B})=\frac{1}{3} \times \frac{10}{36}
$
$\frac{5}{54} \neq \frac{5}{36}$ so not independent
Alternative method for question 1(b)
$\mathrm{P}(\mathrm{B} \mid \mathrm{A})=\mathrm{P}(\mathrm{B})$
$
\mathrm{P}(\mathrm{B} \mid \mathrm{A})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})}=\frac{\frac{5}{36}}{\frac{1}{3}}
$
$\frac{5}{12} \neq \frac{5}{18}$ 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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