Transcript Probability - Cloudfront.net

Dependent Events
Lesson 11-9
Pg. # 436-437
CA Content Standards
Statistics, Data Analysis, and Probability 3.5***
I understand the difference between independent and
dependent events.
Statistics, Data Analysis, and Probability 3.1***:
I represent all possible outcomes for compound events and
express the theoretical probability of each outcome.
Statistics, Data Analysis, and Probability 3.4:
I understand that the probability of one event following
another, in independent trials, is the product of the two
probabilities.
Vocabulary:
DEPENDENT EVENTS
Two events in which the outcome of the
second is affected by the outcome of the
first.
Objective
Find the probability of dependent events.
Math Link: You know how to find the probability
of independent events. Now you will learn how
to find the probability of dependent events.
Example 1.
Find each probability;
imagine that you are
spinning the spinner
two times.
P (red, purple)
P (not red, purple)
P (red, green)
Please note…
We just rehearsed probabilities
involving two events that do not
influence one another; now we are
going to focus on compound events (2
events) in which our actions during the
first event influence the outcome of the
second event.
Example 2.
The school carnival has a dart game. You can win a prize
by hitting 2 red balloons.
What is the probability of
hitting one red balloon
on the first try AND one
red balloon on the
second try?
A Little Background…
Throwing two darts is a compound event.
A compound event is a combination of
two or more simple events.
The outcome of the first dart DOES
influence the outcome of the second
dart. The two spins are dependent
events.
To find P (red, red), find the probability of
each event and multiply.
Step 1. Find each probability.
P (red:1st dart) = 4/8= 1/2
P (red:2nd dart) = 3/7
Step 2. Multiply.
1/ x 3/ = 3/
2
7
14
The probability of winning a prize is 3/14, or 3
out of 14 tries.
Example 3.
In example 2, are you more likely to hit two
red balloons if the first balloon is replaced
before your second throw or if it is not
replaced?
NOT REPLACED: From Example 2, we
know that the probability of hitting two red
balloons if the balloon is not replaced is 3
out of 14, or 21%.
REPLACED: To find P (red, red), find the
probability of each event and multiply.
Step 1. Find each probability.
P (red:1st dart) = 4/8= 1/2
P (red:2nd dart) = 4/8= 1/2
Step 2. Multiply.
1/ x 1/ = 1/
2
2
4
The probability of winning a prize is 1/4, or 25%, if
the balloon is replaced. Therefore, we have a
greater chance of winning if the balloon is
replaced before the second dart.
Example 4.
The letters of the word MATHEMATICS were
placed in a bag; find the probability of forming
the word AT if the first letter is put back before
picking the second letter.
Step 1. Find each probability.
P (A) = 2/11
P (T) = 2/11
Step 2. Multiply.
2/ x 2/ = 4/
11
11
121
Example 5.
The letters of the word MATHEMATICS were
placed in a bag; find the P (H, C) if the first
letter is NOT put back before picking the
second letter.
Step 1. Find each probability.
P (H- First draw)= 1/11 P (C- Second draw)=1/10
Step 2. Multiply.
1/ x 1/
1/
=
11
10
110
Moral of the Story
For dependent events, the outcome of
the first event affects the outcome of the
second event.