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Expert: - 9/1/2011


Question
Problem 1 Image
Problem 1 Image
Hello. How are you? Will you check to see if these answers are correct?

Problem 1 - A simple dartboard has three areas… the main board has a radius of 11 inches, there is a circle with a radius of 5 inches, and the bullseye has a radius of 3 inches. What is the probability of a random dart landing inside the bullseye? Round to the nearest thousandth. (Hint: Use A = π r²)

My answer:
Bullseye = (pi)*3^2
Board = (pi)*11^2
P(land in bullseye) = [(pi)*9]/[(pi)*121] = 9/121 = 0.074

Problem 2 - Last fall, a gardener planted 87 iris bulbs. She found that only 72 of the bulbs bloomed in the spring.
1. Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.
2. How many of the bulbs should she plant next fall if she would like at least 88 to bloom?

My answer:
72/87 = 24/29
24/29x = 88
x = 106.33
107 bulbs

Problem 3 - A community 5K run will award $50 to the winner. 65 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.

My answer:
Expectation = chance of win times entry fee - chance of loss times entry fee.
Expectation = (1/65)($20) - (64/65)($20)
Expectation = $0.31 - $19.69
Expectation = - $19.38
A fair entry price is $19.38

Problem 4 - According to the U. S. Census Bureau, the total 2008 U.S. population was 303,824,640. The chart below summarizes the 2008 population for five U.S. States.

State          2008 Population
Missouri          5,911,605
Pennsylvania      12,448,279
Tennessee          6,214,888
Utah          2,736,424
Washington         6,549,224

What is the probability that a randomly selected U.S. resident did not live in Washington?
Round solution to the nearest thousandth.

My answer:
= (total-Washington)/total
= (303824640-6549224)/303824640
= 0.978

Answer
Questioner:Miss Susan Wilson
Country:Texas, United States
Category:Advanced Math
Private:No
Subject:Probability
Question:

Hello. How are you? Will you check to see if these answers are correct?

Problem 1 - A simple dartboard has three areas… the main board has a radius of 11 inches, there is a circle with a radius of 5 inches, and the bullseye has a radius of 3 inches. What is the probability of a random dart landing inside the bullseye PROVIDED IT HITS THE BOARD? Round to the nearest thousandth. (Hint: Use A = π r²)  <<< You really need this hint?

My answer:
Bullseye AREA = (pi)*3^2
Board AREA = (pi)*11^2
P(land in bullseye) = [(pi)*9]/[(pi)*121] = 9/121 = 0.074

>>>>>>>>>>>>> Yes, that looks OK.

Problem 2 - Last fall, a gardener planted 87 iris bulbs. She found that only 72 of the bulbs bloomed in the spring.
1. Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.
2. How many of the bulbs should she plant next fall if she would like at least 88 to bloom?

My answer:
72/87 = 24/29   << part 1?
24/29x = 88
x = 106.33
107 bulbs

>>>>>>>>>>>>> STill looks OK.

Problem 3 - A community 5K run will award $50 to the winner. 65 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.

My answer:
Expectation = chance of win times entry fee - chance of loss times entry fee.

NO GOOD.

Expectation = chance of win times PROFIT FOR WINNING - chance of loss times entry fee.
Expectation = (1/65)($THIRTY) - (64/65)($20)
Expectation = $0.31 - $19.69
Expectation = - $19.38
A fair entry price is $19.38

I DO NOT AGREE.

A fair price will produce an expectation of zero.

The average winning payoff is 50/65 dollars.  That is the fair price.



Problem 4 - According to the U. S. Census Bureau, the total 2008 U.S. population was 303,824,640. The chart below summarizes the 2008 population for five U.S. States.

State          2008 Population
Missouri          5,911,605
Pennsylvania      12,448,279
Tennessee          6,214,888
Utah          2,736,424
Washington         6,549,224

What is the probability that a randomly selected U.S. resident did not live in Washington?
Round solution to the nearest thousandth.

My answer:
= (total-Washington)/total
= (303824640-6549224)/303824640
= 0.978

>>>>>>>>>>>> Looks OK.

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

Education/Credentials
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