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 $\mathrm{A}$ 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?
Throughout this solution, we convert the statements about probability to fractions of the populations in question.

Since 2000 people are asked about side effects and $\frac{3}{25}$ of these people have severe side effects, then the number of people with severe side effects is $\frac{3}{25} \cdot 2000=240$.

Since 240 have severe side effects and $\frac{2}{3}$ of them were given Medicine A, then the number of people who were given Medicine A that have severe side effects is $\frac{2}{3} \cdot 240=160$.

This means that the number of people who were given Medicine B and have severe side effects is $240-160=80$.

|  | Medicine A | Medicine B | TOTAL |
| :---: | :---: | :---: | :---: |
| Mild side effects |  |  |  |
| Severe side effects | 160 | 80 | 240 |
| TOTAL |  |  |  |

Since 1000 people were given Medicine A and $\frac{19}{100}$ have severe or mild side effects, then the number of people who were given Medicine A that have severe or mild side effects is 190 . This means that the number of people who were given Medicine A that have mild side effects is $190-160=30$.

|  | Medicine A | Medicine B | TOTAL |
| :---: | :---: | :---: | :---: |
| Mild side effects | 30 |  |  |
| Severe side effects | 160 | 80 | 240 |
| TOTAL | 190 |  |  |

Similarly, the number of people who were given Medicine B that have severe or mild side effects is $\frac{3}{20} \cdot 1000=150$, of whom 80 have severe side effects and so $150-80=70$ have mild side effects.

|  | Medicine A | Medicine B | TOTAL |
| :---: | :---: | :---: | :---: |
| Mild side effects | 30 | 70 |  |
| Severe side effects | 160 | 80 | 240 |
| TOTAL | 190 | 150 |  |

Since 30 people with mild side effects were given Medicine A and 70 were given Medicine B, then the probability that a random person with mild side effects was given Medicine B is $\frac{70}{70+30}=\frac{70}{100}=\frac{7}{10}$.

ANSWER: $\frac{7}{10}$