Quote:

The personnel department of a company has records

which show the following analysis of its 200 engineers.

$\displaystyle \begin{array}{cccccccc}\text{Age} &|& \text{BS} &|& \text{MS} &|& \text{Total} & | \\ \hline \text{under 30} &|& 90 &|& 10 &|& 100 &| \\

\text{ 30-40} &|& 20 &|& 30 &|& 50 &| \\ \text{over 40} &|& 40 &|& 10 &|& 20 &| \\ \hline \text{Total} &|& 150 &|& 50 &|& 200 &| \end{array}$

If one engineer is selected at random from the company, find:

1. The probability that he has only a BS.

2. The probability that he has an MS, given that he is over 40.

3. The probability that he is under 30, given that he has only a BS.