Download NC Math 2 Probability Day 1 Name #______ (1) Suppose a red die

NC Math 2
Probability Day 1
Name _______________________________________ #________
(1) Suppose a red die and a green die are rolled at the
same time.
(a) What does the entry “3, 2” in the chart mean?
(b) Complete the chart to the right, showing all the
possible outcomes of a single roll of two dice.
(c) How many possible outcomes are there? ________
(d) What is the probability of rolling a (1, 2), that is, a 1
on the red die and a 2 on the green die? __________
What is the probability of rolling a (2, 1)? _______
What is the probability of rolling a (4, 4)? _______
The chart you completed in question 1 is called a sample space for the situation of rolling two dice. A
sample space is the set of all possible outcomes. For fair dice, all 36 outcomes in the sample space are
equally likely to occur. Equally likely means that each outcome has the same probability. When
outcomes are equally likely, the probability of an event is given by:
𝑃(𝑒𝑣𝑒𝑛𝑡) =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑓𝑢𝑙 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
(2) If two dice are rolled, what is the probability of getting: (use the sample space above to help answer these questions)
(a) doubles? __________
(b) a sum of 7? ___________
(d) doubles and a sum of 8? ____________
(f) a sum no more than 9? ___________
(c) a sum of 11? ___________
(e) doubles or a sum of 8? ____________
(g) a sum of at least 9? ___________
(h) a sum of 2 or 3? _______
A probability distribution is a description of all possible numerical outcomes of a random situation,
along with the probability that each occurs. A probability distribution differs from a sample space in that
all the outcomes must be a single number and the probabilities must be specified. For example, the
probability distribution table below shows all possible sums that you could get from the roll of two dice.
Probability Distribution for the Sum of Two Dice
Sum
2
3
4
5
6
7
8
9
10
Probability
(3) Use the sample space in question 1 to fill in the probabilities on the chart above.
(4) What is the sum of all the probabilities? _________
11
12
(5) Suppose that you roll two dice and record the larger of the two numbers. (If the numbers are the
same, record that number.)
(a) Complete the table below to create the sample
space for this new problem.
(b) Use the sample space you created to complete
the probability distribution below.
Probability Distribution of Larger of Two Rolled Dice
Larger
Die
Probability
(c) What is the probability that the larger of the two numbers is 3? ____________
What is the probability that the larger of the two numbers is 2 or 3? __________
What is the probability that the larger of the two numbers is 3 or less? _________
(6) Now, suppose you roll two dice and record the absolute value of the difference of the two numbers.
(a) Complete the table below to create the sample
space for this new problem.
(b) Use the sample space you created to complete
the probability distribution below.
Probability Dist. of Absolute Value of the Difference
Absolute
Value of
Probability
Difference
(c) What is the probability that the absolute value of the difference is 3? ___________
(d) What is the probability that the absolute value of the difference is at least 2? ___________
(7) Now, suppose you flip a coin twice.
(a) Complete the table below to create the sample
space for this new problem.
(b) Use the sample space you created to complete
the probability distribution below.
Probability Distribution for the Number of Heads
Number
of Heads
Probability
(8) Suppose you flip a coin three times.
(a) Make a list of all 8 possible outcomes.
Are all these outcomes equally likely? _______________
(b) Make a probability distribution (similar to question 7b)
for the number heads for three coins in the space to the right.
(c) What is probability that you will get exactly two heads? _________ At most two heads? __________
(9) Some games use a die in the shape of a regular tetrahedron (four faces) and the numbers 1, 2, 3, and
4 on it. Suppose you roll this die twice.
(a) Make a chart that shows the sample space of all
possible outcomes in the space below.
(b) Make a probability distribution table for the difference
of the two rolls (first roll – second roll) in the space below.
(c) What difference are you most likely to get? ________
(d) What is the probability that the difference is at most 2? _____________
(e) What is the probability that you get a difference of 3 or you get a 2 on the first die? _________
(f) What is the probability that you get a difference of 2 or you get doubles? ___________