STAtistics / Mr. Hansen

Name: _______________________________________

1/5/2010

 

 

CFU on Probability

 

1.

Cornstalks in a field have a mean height of 7 feet and a standard deviation of 3 inches. Two stalks are independently selected from the field.

 

 

(a)

Compute the probability that the first stalk chosen is taller than 83.2 inches. Show adequate work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)

Compute the probability that at least one of the first two stalks chosen is taller than 87 inches. Show work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c)

Compute the probability that both of the first two stalks chosen are shorter than 83.2 inches. Show work.

 

 

 

 

 

 

 

 

 

 

 

 

2.

In the universe of students, the probability of diligence (event D) is 0.4, and one fourth of students earn an A (event A). Among the students, 55% are diligent or earn an A (or both). Draw a Venn diagram to illustrate the universe, as well as the relationship among events A and D. Use the blank region below.


















Also state the following to 3 decimal places of accuracy:
P(A Ç ~D) = _______
P(A | D) = _______
P(D | ~A) = _______
P(D) = _______
P(~A È ~D) = _______

Explain carefully why A and D are independent but not mutually exclusive. Label the probabilities that you use in your proof.

 

 

 

3.

Two fair dice are rolled.

 

 

(a)

Compute the unconditional probability of an even sum. Work is required for credit.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)

Now suppose that I can see the outcome of the roll of the dice, but you cannot. You ask me, “Mr. Hansen, is at least one of the two dice showing an even number?” I respond, “Yes.” Does this increase or decrease the likelihood that the sum of the two dice is even, or does the probability remain the same? Show your work (no credit without work).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.

I feel lucky, and I think I can roll an 8 on my next roll of the dice. You think this is unlikely, and you offer me odds of 6:1. Is this a fair game? _______ Compute the expected value of the game to me for each dollar that I wager. (Work is needed for credit.)

 

 

5.

Mr. Hansen’s brother is a good free-throw shooter. His probability of success is 0.92.

 

 

(a)

Compute the probability of at least 4 successes in 6 shots.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)

Compute the probability that the first success occurs on or after the third shot.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c)

Compute the probability of at least one success in 4 shots.