# statistics calculating probabilities

2.1 Calculating Basic Probabilities

Supplies Needed: 2 dice (6-sided). If you do not have dice, or prefer to use an online die roller, you can use www.dicesimulator.com.

Show work when applicable.

Use only 1 die to complete the following:

1. Roll the die one time. What number did you get? __________

2. How many different outcomes were possible when you rolled the die? __________

3. List the sample space for the single die roll “experiment”. ________________

4. What is the probability that you would get a 4 in this experiment? P(4) =_____

Now use 2 dice to complete the following:

5. Roll both dice at the same time and add their results. What number did you get? __________

6. How many different outcomes (total of the two dice) were possible? __________

7. Complete a 2-dice outcome grid which shows all of the possibilities when rolling 2 dice: (Hint: Grid will be 6 rows by 6 columns).

THE 2-DICE OUTCOME GRID: When rolling two dice and adding their results, we know that it is only possible to get the numbers 2-12. However, this 2- dice outcome grid shows us that there are 36 different ways that you can roll two dice. Notice that there is only one way that you can roll a sum of 2. This only happens when both dice outcomes are 1. Therefore, there is only 1 way out of 36 options that we can roll a sum of 2. Mathematically, we write this as: P(2) = 1/36

Find the following Probabilities:

P(3) =

P(4) =

P(5) =

P(6) =

P(7) =

P(12) =

What is the most likely result?

Section 2.1

1. How many different ways can we express probabilities? ________________

2. What are the different ways to express probabilities? ________________ ________________

3. If you roll a normal 6-sided die ten times and you get a 3 every time, what is the probability that you will roll a 3 on your next roll? ________________

4. How many cards are in a standard deck of playing cards? ________________

5. What is the probability of being dealt a red 5 if you are dealt one card?

c. Write your answer as a decimal (round to the nearest thousandth). _______________

6. Important: The following all mean the same thing – find the probability that you do not get a 2.

P(~2)

P(not 2)

P(2c )

Complement of getting a 2

To Solve these problems, you can find the following: 1 – P(2)

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