UNIT 6 HOMEWORK
Math 102 & Core 143
Note: All data below is ficticious.
1. Complete the following table regarding tossing a fair coin and counting the number of heads.
|Number of heads |Percent of heads
Number of tosses |Expected value |SEsum |Expected value |SE%
100 |50 |5|50% |5%
2500 | | | | 1%
10000 | | | |
1000000 | | | |
2. A box contains 1 zero and 9 ones. True or false and justify your answer.
i) If we draw 10 times we have a better chance of getting exactly 1 zero than the chance of getting
exactly 10 zeros on 100 draws.
ii) If we draw 100 times we have a better chance of getting exactly 10 zeros than the chance of
getting exactly 100 zeros on 1000 draws.
iii) If we draw 10 times we will get closer to 10% zeros than if we draw 10000 times.
3. In gambling, the following is a commonly held belief. If a gambler has lost 10 times in a row,
then the gambler should continue playing because he is due to win, by the law of averages. Explain
why this reasoning is incorrect.
4. Create box models for each of the following situations.
i) We roll 20 dice and want to add the sum of the values rolled.
ii) We roll a pair dice and win $1 if the sum is greater than or equal to 10. We lose $1 otherwise.
This game is played 50 times.
5. True or false: We flip a fair coin 100 times. The chance that we get exactly 50 heads is less than
the chance that we get exactly 50% heads.
6. Consider a box with the numbers 1,2,7,9,9,10 in it. We draw 100 times (with replacement).
i) What is the chance that the sum of draws is less than 100?
ii) What is the chance that the sum of draws is greater than 1000?
iii) What is the approximate chance that the sum of draws is between 650 and 750?
7. We bet $1 on roulette and have a 12
38 chance of winning. If we win, we win $2 (otherwise, we lose
our $1). We play this game 100 times. Fill in the blanks:
We expect to win/lose (circle one) $ , give or take $ .
8. You roll a die 180 times and count the number of !
•’s.
i) Fill in the blanks: We expect to get !
•’s., give or take !
•’s.
ii) If we gather a large group of people to each do the above experiment (roll a die 180 times and
count the number of !
•’s), about what percentage of these people should get an answer between 15
and 45?
