Environmental engineers classify U. S. consumers into five groups based on consumers’ feelings about environmentalism:
Basic Browns claim they don’t have the knowledge to understand environmental problems.
True-blue greens use biodegradable products.
Greenback greens support requiring new cars to run on alternative fuel.
Sprouts recycle newspapers regularly.
Grousers believe industries, not individuals, should solve environmental problems.
Assume the proportion of consumers in each group is shown in the table below. Suppose a U. S. consumer is selected at random and his/her feelings about environmentalism is determined.

Basic browns 0.28

True-blue greens 0.11

Greenback greens 0.11

Sprouts 0.26

Grousers 0.24

List the simple events for the experiment.
Assign reasonable probabilities to the simple events.
Find the probability that the consumer is either a basic brown or a grouser
Find the probability that the consumer supports environmentalism in some fashion (i. e., the consumer is a true-blue green, a greenback green, or a sprout).
2. A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 30%, 20%, and 50%, respectively, of all jobs bid by the company. For i = 1, 2, 3, define Ei to be the event that a job is estimated by engineer i. The following probabilities describe the rates at which the engineers make serious errors in estimating costs:

P(error | E1) = 0.01, P(error | E2) = 0.03, and P(error | E3) = 0.02

If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 1?
If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 2?
If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 3?
Based on the probabilities, parts (a) – (c), which engineer is most likely responsible for making the serious mistake?
3. Suppose there are six gasoline pumps at a gas station. Let Y be the number of pumps in use during the lunch hour. The probability distribution of Y is given in the table below. SHOW WORK!

Y

0

1

2

3

4

5

6

P(y)

0.03

0.09

0.25

0.33

0.15

0.08

0.07

What is the probability that at a given time at least three pumps are in use?
What is the probability that at a given time there are exactly four pumps in use?
What is the expected number of pumps in use?
What is the standard deviation of Y?