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Quiz 10 Review
Name:
Standard(s) assessed
8. Law of Large Numbers


Score
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
9. Computing Probabilities

Compute probabilities using an appropriate sample space

Compute probabilities using counting rules including
permutations and combinations
10. Compound Events

Solve compound probability problems using tree diagrams and
area diagrams

Use conditional probabilities – level 1
11. Expected Value

Compute expected value

Make and defend decisions based on expected value
calculations
Law of Large Numbers
1.
A coin is flipped some number of times and the result was 80% heads. Is it more likely
that the coin was flipped 10 times or 1000 times? Explain
Computing Probabilities
2.
Alice has 5 red, 6 blue, 3 white, and 4 orange marbles. All marbles are put in a sack and
one marble is selected at random. Compute each probability.
a. P(red) = _______
b. P(blue) = _______
c. P(red or orange) = _______
d. P(not getting white) = _______
3.
4.
Two four-sided dice are rolled.
a.
List all the possible outcomes (sample space) using table.
b.
Calculate the probability that both dice show the same number.
c.
Calculate the probability of rolling a sum of 5.
In calculating the probability of rolling a sum of seven on a pair of dice, why is it
inappropriate to use the sample space S = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }?
Compound Events
5.
6.
A coin is tossed and a die is rolled. What is the probability that . . .
a.
The coin lands “heads” and the die shows a six?
b.
the coin lands “heads” or the die shows a six?
A bag contains 4 blue marbles and 5 red marbles. Suppose you were to reach in
and select three marbles at random.
a.
Make a tree diagram to show the possible outcomes.
b.
Label the probabilities on each branch of the tree diagram.
c.
Show how to calculate the probability that all marbles are red.
d.
Show how to calculate the probability that the first two are blue and the
third is red.
e.
Calculate the probability that at least one of the marbles is blue.
7.
BASKETBALL One-and-one
Create a rug diagram or a tree diagram for the following one-and-one situation.
Liz has a 65% chance of making the 1st shot. If she makes the first shot, she has a 70%
chance of making the 2nd shot.
Calculate the probabilities
P( 0 points) =
P(1 point) =
P(2 points) =
Expected Value
8.
Calculate the expected number of points for Liz in a one-and-one situation above.
9.
Use the table to compute the expected value.
a.
10.
X
P(X)
3
.5
1
.1
-1
.4
X
P(X)
1
.1
2
.3
3
.6
In the Pennsylvania Lottery’s Big 4, a $1 ticket gives you a chance to win
$5000 if you guess the correct number. What is the value of a $1 lottery
ticket? Compute the expected value for your winnings. (Do not include the
price of the ticket in your calculation.