Download SOL 6.16 Probability NOTEPAGE

SOL 6.16 Probability and Statistics
NOTEPAGE FOR STUDENT
Page 1
Probability
Probability is that part of math that describes the chance that a certain event will happen
or not happen.
The probability of an event occurring is equal to the desired outcomes divided by the
total number of possible outcomes. The total number of outcomes is also called the sample
space. This is what it looks like in a formula:
P (event) =
Desired Outcomes
The Total Number Of Possible Outcomes
Therefore, the probability of rolling a number cube and getting an even number is
3
.
6
There are 6 possible outcomes (1, 2, 3, 4, 5, 6).
There are 3 desired outcomes (2, 4, 6).
The fraction
3
is actually a special kind of fraction called a ratio. It is read 3 out of 6.
6
As we are looking at just one event, this is called a simple event.
We can show the probability of an event as a ratio, a decimal, or a percent. If we use
the example above, the probability of rolling an even number can be represented in fraction
form as
3
or in decimal form as .5 or in percent form as 50% .
6
The probability of an event occurring is a fractional number or ratio between and
including 0 and 1.
A probability of 0 means the event will never occur.
Suppose we were asked to find the probability of rolling a 7 on a number cube. This would
be a probability of 0. It is impossible to roll a 7 because the numbers on a number cube
only range from 1 to 6.
A probability of 1 means the event will always occur. If we were asked to determine
the probability of rolling a number less than 7, then there would be a probability of 1. It is
certain to happen because all of the faces on a number cube represent numbers that are
less than 7.
©2011
SOL 6.16 Probability and Statistics
NOTEPAGE FOR STUDENT
Page 2
Probability
Sample Space
Keep in mind a sample space represents all possible outcomes of an experiment and can
be organized by using a list, tree diagram, picture, or chart.
The sample space for
flipping a coin is heads or tails because when we flip a coin, it can only land on heads or
tails.
Independent vs. Dependent Events
Independent events happen when the outcome of one event has no effect on any other
events. Independent events could include flipping a coin or rolling a number cube. It
doesn’t matter how many times we roll or flip the coin or cube. It will not affect the next
outcome. To calculate the probability of two independent events, we need to use the
following formula:
P (A and B) = P(A) · P(B)
Probability
of Event A
Probability
of Event B
We discovered above that the probability of rolling an even number on a number cube is
3
.
6
How about rolling two even numbers in a row?
P(even and even) =
3 3
1
9
·
=
=
6 6
4
36
Simplify.
P (A and B) = P(A) · P(B)
Probability
of Event A
Probability
of Event B
What are the chances of rolling a “6” on the first roll and an odd number on the second roll?
P(6 and odd) =
1 3
1
3
·
=
=
6 6
36 12
©2011
Simplify.
SOL 6.16 Probability and Statistics
NOTEPAGE FOR STUDENT
Page 3
Probability
Dependent events happen when the outcome of one event affects another. The
formula for calculating the probability of a two dependent events is:
P (A and B) = P(A) · P(B after A)
Probability
of Event A
Probability of
Event B after
Event A
A box of popsicles is opened at a pool party. We are crossing our fingers for a grape. We
know there are only three grape popsicles in that box, and there are a lot of swimmers in
front of us. What is the probability that we will get a purple popsicle?
Example: Let’s use the purple popsicle situation to better understand dependent events.
First, let’s consider the chances of getting a purple popsicle out of a box that contains 12
popsicles. Out of 12 popsicles, only 3 are purple.
The probability of this simple event is 3 out of 12 or
1
3
3
Simplify:
=
4
12
12
However . . . let’s say five other swimmers have pulled popsicles out of the box at the pool
party and one of them is purple! One of us get the next popsicle, and another swimmer
behind us also wants a purple. What are the chances that both of us get purple popsicles?
P (A and B) = P(A) · P(B after A)
2 1
2
1
P(purple and purple) =
·
=
=
7 6
42
21
Good luck with
those chances!
Probability of picking a
Probability of another swimmer picking
purple popsicle with 5
another purple with 6 popsicles already
popsicles already picked
picked out of a box of 12 (2 of them
out of a box of 12 (1 of
purple).
them purple).
3 purple pops – 1 picked – 1 possible = 1
3 purple pops – 1 picked = 2
12 total pops – 6 picked
12 total pops – 5 picked = 7
©2011
=6
SOL 6.16 Probability and Statistics
NOTEPAGE FOR STUDENT
Page 4
Probability
PRACTICE!
Identify whether each situation below is an independent or dependent event? Be
prepared to defend your answer to a partner.
1. Land on a particular number on a spinner.
2. Draw cards from a deck (and replacing them).
3. Draw cards from a deck (without replacing them).
4. Select candies from a bag.
5. Choose a marble from a bowl and putting it back.
6. Choose a marble from a bowl without putting it back.
©2011