Math 010
10.3 Notes for Final Exam
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Probability is a measure of the likelihood of an event. It is always between 0 and 1 (or 0% and 100%).
A probability of 0 means the event will definitely not happen.
A probability of 1 (or 100%) means the event will definitely happen.
To calculate probability, create a fraction. The numerator is the number of outcomes in the desired event,
and the denominator is the total number of outcomes.
Example: There are ten marbles in a bag. Three of them are blue. If you pull a marble out at random, what is
the probability of that marble being blue?
Favorable outcomes = 3
Possible outcomes = 10
3
P(marble is blue) = 10
Note: Random is a theoretical concept which means each possible outcome has an equal likelihood of
happening. In the real world, there is no such thing as random because many factors influence the likelihood
of events.
Odds in favor is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
Using the same example, what are the odds in favor of the marble being blue?
Favorable outcomes = 3
Unfavorable outcomes = 10 – 3 = 7
3
Odds in favor = 7
Odds against is the ratio of the number of unfavorable outcomes to the number of favorable outcomes. It is
the reciprocal of odds in favor. What are the odds against the marble being blue?
Favorable outcomes = 3
Unfavorable outcomes = 10 – 3 = 7
7
Odds in favor = 3 or “seven to three”
Name(s): _______________________________________________________________________
Math 010 Probability Activity (Quiz Grade for 12/4/13)
There are 36 possible outcomes from rolling two dice.
You will notice that if you add the values of both dice together to obtain a number of points, you will get a number
between 2 and 12. There is only one way to roll a 2 (snake eyes), and only one way to roll a 12 (two sixes). For the other
numbers, there are multiple ways they can be rolled.
What is the theoretical probability of rolling a 7?
To find this probability, you need to create a fraction. First count the number of possible outcomes where you would
roll a 7. This is your numerator. The denominator will be the number of total possible outcomes, 36.
Find the fraction and simplify:
In the table below, list the probabilities of rolling each of the values (all fractions must be simplified):
Roll
2
3
4
5
6
7
8
9
10
11
12
Probability
You will conduct an experiment to see if these probabilities reflect what happens in reality. This is an experiment to
determine whether dice are “fair”. Roll a pair of dice 100 times. Record the outcomes (sum of both dice) in the
frequency table below.
Roll
2
3
4
5
6
7
8
9
10
11
12
Tally
Frequency
In the space below, draw a histogram that illustrates these results. Also answer these questions:


What does your histogram tell you about the distribution of roll values? Is it skewed, normal, or evenly
distributed?
How do your results compare with the theoretical possibilities you found on the first page?