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 Turn In Problems 
 Business Decisions — Likelihood 

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

- Nikolay Konstantinov

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1. When rolling two dice, what is the probability of the sum being an even number?

0.05 50% 1 to 1 2 to 1

2. When rolling two dice, whatare the odds of the sum being an even number?

0.05 50% 1 to 1 2 to 1

3. When rolling two dice, what is the probability of the sum being 8 or more?

15% 42% 58% 85%

4. When rolling two dice, what are the odds of the sum being 8 or more?

5 to 7 7 to 5 15 to 36 36 to 15

5. The medicine trastuzumab, which fights breast cancer in women who already have breast cancer, was popularized because of a certain study. In the control group of 1,700 women, 34 died. In the group treated with trastuzumab, 23 of 1,643 women died. What percentage of the women in the control group died? What percentage of the women in the treated group died?

0.02% and 0.014%
0.2% and 0.14%
2% and 1.4%
20% and 14%

6. Continuing the previous problem, what was the absolute change (subtraction) in risk?

0.06% 0.6% 6% 60%

7. Continuing the previous problem, what was the relative change (percent change) in risk?

3% 30% 33% 43%

8. Trastuzumab also has some dangerous side effects. Most notably, 40% of the women who take it develop flu-like symptoms, 7% develop mild heart problems, and 5% suffer a stroke or severe heart failure. About how many of the 1,643 women in the study who were treated with trastuzumab suffered a stroke or severe heart failure because of drug?

3 women 8 women 33 women 82 women

9. Your little brother thinks that ten is a very big number. He wants to play a dice game about the number ten. He proposes a game where you each start with a pile of candies, and he finds the sum of two dice several times. Whenever the sum is less than ten, he gives you one candy. Whenever the sum is ten or greater, you give him more than one candy—but he is not sure how many is fair. Help your brother finish inventing his game by using an expected value table to find how many candies must you give him when he "wins" so that the game has an expected value of zero.

5 candies 6 candies 8 candies 10 candies

10. Your friend is starting a food cart business. She has read that new food carts have a 35% chance to go out of business during the first year with a $10,000 loss, a 30% chance to earn $20,000 profit the first year, a 15% chance to earn $30,000 profit the first year, a 15% chance to earn $40,000 profit the first year, and a 5% chance to earn $50,000 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?

$13,000 $15,500 $22,500 $130,000