Question

A small town gets its water supply from three nearby lakes, A, B, and C. Sometimes in the late summer

the water level in a lake falls below a certain critical level. When this occurs, there is a risk that the water

from that lake will become polluted with E-Coli. If the water supply to the town becomes polluted, the

residents are advised to boil their water. If only the water level at lake A falls below the critical level,

experience has shown that the residents will have a 5% chance of a boil water advisory. Similarly, if

only the water levels at lakes B or C fall below the critical level, chances of a boil water advisory are

4% and 7%, respectively. If two or more lakes fall below the critical levels simultaneously, the risk

of a boil water advisory rises to 40%. Lake A falls below the critical level in 30% of the summers,

while this number is 50% and 20% for lakes B and C, respectively. The probability that exactly two

lakes will fall below their critical levels simultaneously is 12%, and it is equally likely to be any two of

the three. Finally, there is a 3% chance that all three lakes will simultaneously fall below their critical

levels. During some summer in the future:

a) What is the probability that the residents will have a boil water advisory?

b) If the residents have a boil water advisory, what is the probability that the water level will fall

below the critical level at lake B alone?

c) If the residents have a boil water advisory, what is the probability that the water level will fall

below the critical levels at two or more lakes simultaneously?

Answer 1