CSMC 2021 Part A - Question 4, CEMC UWaterloo

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Difficulty: 5

This problem is tagged with csmc, csmc21, highschool.

(Canadian Senior Mathematics Contest 2021, Part A, Question 4, CEMC - UWaterloo)

In an experiment, $1000$ people receive Medicine $A$ and $1000$ different people receive Medicine $B$. The $2000$ people are asked whether they have severe side effects, mild side effects, or no side effects. The following information is obtained from the experiment:
$(i)$ The probability that a random person has severe side effects is $\frac{3}{25}$.
$(ii)$ The probability that a random person with severe side effects was given Medicine $A$ is $\frac{2}{3}$.
$(iii)$ The probability that a random person who was given Medicine $A$ has severe or mild side effects is $\frac{19}{100}$.
$(iv)$ The probability that a random person who was given Medicine $B$ has severe or mild side effects is $\frac{3}{20}$.
What is the probability that a random person with mild side effects was given Medicine $B$?

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Type your answer in fractional form, as "x/y".

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