Transcript Probability - Cloudfront.net

Probability
Lesson 11-1
Pg. # 418-419
CA Content Standards
Statistics, Data Analysis, and Probability 3.3 ***:
I represent probabilities as ratios; I know that if P
is the probability of an event, 1- P is the
probability of an event not occurring.
Mathematical Reasoning 3.1:
I evaluate the reasonableness of the solution in
the context of the original situation.
Review Vocabulary: Ratio
A comparison of two quantities.
Note: These CANNOT be any two
quantities written in any order. In a ratio, the
choice of quantities is VERY important.
Notation [how you can write a ratio]:
(1) 16 to 10
(2) 16:10
(3) 16/10
Vocabulary: PROBABILITY
A measure of how likely it is that some
event will occur.
Ratio: Number of favorable outcomes
Number of all possible outcomes
Vocabulary: CERTAIN EVENT
An event that is sure to happen.
Has a probability of 1.
For example:
Probability (green) = 5 = 1
5
Vocabulary:
IMPOSSIBLE EVENT
An event that cannot happen.
Has a probability of 0.
For example:
Probability (orange) = 0 = 0
5
Objective
Write a ratio to represent the probability that an
event will or will not happen.
Math Link: You learned to write a ratio
comparing two quantities. Now you will write a
ratio to represent the probability that something
will happen.
Example 1.
What is the probability that the spinner will
land on green?
P(green) = favorable outcomes
possible outcomes
P(green) = 4 green
8 total
P(green) = 4 = 1
8 2
Example 2.
What is the probability that the spinner will NOT land on
yellow?
First find the probability that the spinner will land on
yellow.
P(yellow) = favorable outcomes
possible outcomes
P(yellow) = 2 = 1
8 4
P(not yellow) = 1 - P(yellow)
= 1 - 1 /4
= 3/ 4
Here’s Why It Works
P(not yellow) means the spinner can land on any
color but yellow… including green, red, and blue.
There are 6 sections that are not yellow.
P(not yellow) = 6/8
Each outcome is either yellow or not yellow, so:
P(yellow) + P(not yellow) = 2/8 + 6/8 = 8/8 =1
Therefore, P(not yellow) = 1 - P(yellow)
Example 3.
What is the probability the spinner will land on green
or red.
Since five sections are either green or red…
P(green or red) = favorable outcomes
possible outcomes
P(green or red) = 5
8
CHALLENGE:
Find P(green AND red)
Moral of the Story
We write a ratio to represent the
probability that an event will or will not
occur.