# Prob Qn'

• Apr 10th 2008, 06:44 AM
matty888
Prob Qn'
In testing the water supply for various cities for two kinds of impurities commonly found in water, it was found that 40% had an impurity of type A and 50% had an impurity of type B. 20% of the water supplies had neither sort of impurity (that is 20% did not have type A impurity and it did not have type B impurity). If a city is chosen at random, what is the probability that its water supply has exactly one type of impurity?
• Apr 10th 2008, 11:51 PM
mr fantastic
Quote:

Originally Posted by matty888
In testing the water supply for various cities for two kinds of impurities commonly found in water, it was found that 40% had an impurity of type A and 50% had an impurity of type B. 20% of the water supplies had neither sort of impurity (that is 20% did not have type A impurity and it did not have type B impurity). If a city is chosen at random, what is the probability that its water supply has exactly one type of impurity?

Draw a Karnaugh table:

$\displaystyle \, \begin{tabular}{l | c | c | c} & A & A$\, '$& \\ \hline B & & & 0.5 \\ \hline B$\, '$& & 0.2 & \\ \hline & 0.4 & & 1 \\ \end{tabular}$

I'm sure you can put in the missing probabilities.

Use the table to get the values of Pr(A and B') and Pr(A' and B). Add these values together.

For checking purposes: I get 0.3 + 0.4 = 0.7.