SOL 7.9, 7.10, 7.11
SOL 7.9: The student will investigate and describe the difference between the experimental probability and theoretical
probability of an event.
The probability of an event is a number from 0 to 1 that measures the chance that an event will occur.
One way to find the probability of an event is to conduct an experiment. Experimental probability is determined by
carrying out a simulation or an experiment.
Experimental probability =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑜𝑢𝑡𝑐𝑜𝑚𝑒 𝑜𝑐𝑐𝑢𝑟𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡
Ex) Play chess 10 times and count the wins. Suppose you win 6 times. Compare the number of occurrences of one
result to the number of trials. That is the probability for that result.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑤𝑜𝑛
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑎𝑚𝑒𝑠 𝑝𝑙𝑎𝑦𝑒𝑑
=
6
10
=
3
5
In experimental probability, as the number of trials increases, the experimental probability gets closer to the theoretical
probability (Law of Large Numbers).
Another type of probability allows you to consider the outcomes of the experiment. The outcome of an experiment is
the result. Theoretical probability is the expected probability and can be found with a formula. It is a theory based on
what you know; not on actually doing an experiment.
Theoretical probability =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Ex) Find the probability of rolling a two or a three when you roll a standard die. Determine the number of ways the
event occurs. In this case, the event is getting a two or a three so there are 2 ways to get the favorable outcome.
Determine the total number of outcomes. There are 6 numbers on the die so there are 6 possible outcomes.
Plug it into the formula:
𝑡𝑤𝑜 𝑜𝑟 𝑡ℎ𝑟𝑒𝑒
2
1
= 6 = 3
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
Probabilities can be expressed as a fraction, a decimal, a ratio, or a percent.
SOL 7.10: The student will determine the probability of compound events, using the Fundamental (Basic) Counting
Principle.
The Fundamental (Basic) Counting Principle is a computational procedure to determine the number of possible
outcomes of several events. It is the product of the number of outcomes for each event that can be chose individually.
Ex) Estella wants to choose her outfit of the day. She has a choice between 4 pairs of pants, 6 shirts, and 3 pairs of
shoes.
Using the Counting Principle: 4 x 6 x 3 = 72 so Estella has 72 different combinations of outfits she can make.
Tree diagrams can be used to illustrate possible outcomes of events. They can be used to support the Fundamental
(Basic) Counting Principle.
Using the Fundamental Counting Principle, there should be 3 x 3 which is 9 different outcomes.
A compound event combines two or more simple events. For example, a bag contains 4 red, 3 green, and 2 blue
marbles. What is the probability of selecting a green and then a blue marble? (Hint: or means to add)
3
2
5
+ 9 = 9 so there is a chance of selecting green or blue 5 times out of every 9 selections
9
Independent events are when the two events do NOT effect one another. The second event does not depend on what
happens in the first event.
Ex) Find the probability of rolling a 2 and then rolling a 3 on the number cube. (Hint: and means to multiply)
1 1
1
x 6 = 36 There is a 1 in 36 chance of rolling a 2 and then rolling a 3.
6
Dependent events is when what happens in the first event will change the outcome of the second event.
Ex) Find the probability of choosing a tootsie roll, eating it and then a skittles if there are 4 tootsie rolls and 5
packs of skittles in the jar.
4
5
20
5
x 8 = 72 = 18 There is a 5 out of 18 chances of choosing a tootsie roll, eating it and then
9
choosing a pack of skittles
SOL 7.11: The student, given data in a practical situation, will
a) Construct and analyze histograms; and
b) Compare and contrast histograms with other types of graphs presenting information from the same data
All graphs tell a story and include a title and labels that describe the data.
A histogram is a form of bar graph in which the categories are consecutive and equal intervals. The length or height of
each bar is determined by the number of data elements frequency falling into a particular interval. Numerical data that
can be characterized using consecutive intervals are best displayed in a histogram. A frequency distribution, or table,
shows how often an item, a number, or range of number occurs. It can be used to construct a histogram.
Students who read Wimpy
Kid
Age
Tally
frequency
group
7-10
7
11-14
7
15 18
3