Quiz 11 Review Name:
Standard(s) assessed / Score6. Basic counting rules
· Use the multiplication and addition rules of counting
· Compute and apply factorials
· Construct and apply tree diagrams and tables
7. Advanced counting rules
· Use combinations and permutations to solve counting problems
· Distinguish between situations where combinations, permutations, or other counting rules apply
8. Law of Large Numbers
· Understand the relative frequency interpretation of probability and the Law of Large Numbers
· Conduct simulations with physical models and random number generators to make empirical estimates of probability
Law of Large Numbers
1. Which is a correct interpretation of the Law of Large Numbers?
(a.) If you flip a coin 10 times and get 9 heads, we expect to get tails on the next toss.
(b.) If you flip a coin a small number of times you are more likely to get close to 50% “heads” than if you flip a coin a large number of times.
(c.) If you flip a coin twice and get “heads” both times, the next flip will most likely come up “tails”
(d.) If you flip a coin 50 times, you probably won’t get exactly 25 “heads” but you are likely to get somewhat close to 50% “heads”
2. Suppose that in a one-and-one situation, Liz has a .27 probability of scoring 2 points. Explain what .27 means as a probability in this context.
3. The “Gambler’s Fallacy” is the false belief that in the long run, chance occurrences will even out. After a long string of loses, the gambler acting under this fallacy beliefs that she is due for a win. It keeps the gambler playing and losing. This false belief about probability is similar to the Law of Large Numbers. Explain the difference between the Gambler’s Fallacy (a false belief about probability) and the Law of Large Numbers (a true understanding of probability).
Basic Counting Rules
4. If Mr. Mellor has 4 shirts and 3 pairs of pants, how many different outfits can he put together? Make a tree diagram to show all the possible outfits.
5. How many 3-digit numbers contain no 4’s? How many 3-digit numbers contain at least one 4?
6. How many ways can 5 T/F questions be answered?
7. How many ways can the letters in the word “COMPUTER” be arranged?
Advanced Counting Problems
8. Three door prizes are to be given to 3 lucky people in a crowd of 100.
a. If the three prizes are identical, in how many ways can this be done?
b. If the three prizes are different (1st , 2nd, and 3rd), in how many ways can this be done?
9. Baskin Robbins has 31 flavors. How many three scoop cones can be made if order is important and flavors cannot be repeated?
10. How many three scoop cones are possible if flavors can be repeated?
11. If an athletic conference has 8 teams and each team will play each other once, how many games will there be?