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Math OER
Week 9 Homework, Part B

The greatest reward for a student is not a good grade. It is the willingness of his teacher to listen to him.

- Nikolay Konstantinov

Answer every question. Try being nice to your eyes and posture by printing this page and working with pencil and paper. Then use the button at the bottom of the page to create a code by processing your answers. Copy-and-paste the code into an e-mail along with the answer to your short answer question.

Keep trying each homework assignment until you get 8 out of 10 or more.


The table below shows the number of credit cards owned by a group of individuals.

ZeroOneTwo or MoreTotal
Male951933
Female18102048
Total27153981

1. If one person in that group is chosen at random, what is the probability that the person is female?

2% 12% 45% 59%

2. If one person in that group is chosen at random, what is the probability that the person is male and has two or more credit cards?

23% 49% 57% 65%

3. If one person in that group with zero credit cards is chosen at random, what is the probability that the person is female?

22% 33% 38% 67% 200%

4. If one person in that group who is female is chosen at random, what is the probability that the person has zero credit cards?

22% 33% 38% 67% 200%

5. A charity is holding a raffle, selling 200 tickets. The ticket costs $5. The one winning ticket holder gets $400. What is the expected value for a person buying one ticket?

OutcomeNumeric ValueProbabilityProduct
Win
Lose
Expected Value:
$1.00 $2.98 − $1.00 − $2.98
$1.08 $3.00 − $1.08 − $3.00

6. If there were three winning tickets for $400 each, what would be the expected value for a person buying one ticket?

OutcomeNumeric ValueProbabilityProduct
Win
Lose
Expected Value:
$1.00 $2.98 − $1.00 − $2.98
$1.08 $3.00 − $1.08 − $3.00

7. A certain bond fund has the following predictions for its value (compared to inflation) when it matures in five years. Find its expected value.

OutcomeNumeric ValueProbabilityProduct
Slight Decrease-$50020%
Slight Increase$50020%
Bigger Inrease$1,00060%
Expected Value:
$60 $200 $600 $800

8. Two kids play a game involving flipping two coins repeatedly. One kid gets a point whenever either coin lands heads (only one point, whether a single-heads or double-heads outcome). The other kid gets several points whenever both coins land tails. How many points should a double-tails result be worth to make this a fair game?

OutcomeNumeric ValueProbabilityProduct
HH
HT
TH
TT
Expected Value:
1.5 points 2 points 3 points 4 points

9. A local club is planning a three-day outdoor fundraising event. The cost to host the event is $5,000. Each day that has good weather would generate $15,000 income that day. However, each day it rains would mean zero income that day. According to the weather forecast, there is a 50% possibility of rain on each of the three days. Assuming that rainy days are independent events, what is the expected value of this fundraising event?

Hint: First complete the list of the eight equally likely outcomes for whether the days have rain or not:
Rain/Rain/Rain, Rain/Rain/No, Rain/No/Rain, ...

OutcomeNumeric ValueProbabilityProduct
Three Rainy Days18 = 0.125
Two Rainy Days38 = 0.375
One Rainy Day
Zero Rainy Days
Expected Value:
$12,250 $17,500 $18,250 $18,750 $21,875

10. Your friend is starting a food cart business. She has read that new food carts have a 40% chance to go out of business during the first year with a $7,500 loss, a 20% chance to earn $10,000 profit the first year, a 20% chance to earn $25,000 profit the first year, a 15% chance to earn $40,000 profit the first year, and a 5% chance to earn $45,000 profit the first year. Assuming these numbers are true, and your friend has typical skill and luck in her new business, what is the expected value of her first year's income?

$12,250 $17,500 $18,250 $18,750 $21,875

Short Answer Question:

Think of a real-life application for expected value that we have not mentioned in class or homework.

(The applications we did mention during class that are not also represented in the homework problems above included gumballs, rainfall and irrigation, airport wait times and food sales, and when a class's grading plan uses weighted averages.)