Transcript Step 1. Find each probability

Independent Events
Lesson 11-7
Pg. # 432-433
CA Content Standards
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.
Number Sense 2.1:
I solve problems involving multiplication of positive fractions.
Statistics, Data Analysis, and Probability 3.3***:
I represent probabilities as ratios and percentages between
0 and 100 and verify that the probabilities computed are
reasonable; I know that if P is the probability of an event,
1-P is the probability of an event not happening.
Vocabulary:
COMPOUND EVENT
An event that is a combination of two or
more single events.
Vocabulary:
INDEPENDENT EVENTS
Two events in which the outcome of the
second is not affected by the outcome of
the first.
Objective
Find the probability that two independent events
will occur.
Math Link: You know how to find the probability
that an event will occur. Now you will learn how
to find the probability that two events will occur.
Example 1.
Find each probability.
P (red or purple)
P (not red or purple)
Which is greater:
P (red or green) or
P (not red or green)?
Please note…
We just rehearsed probabilities
involving one event OR another event
(addition); this lesson will focus on
probabilities involving one event AND
another event (multiplication).
Example 2.
The school carnival has a spinner game. You can win a
prize by spinning an A on the first spinner and then yellow
on the second spinner. What is the probability of winning a
prize?
A
B
C
A Little Background…
Spinning both spinners is a compound
event. A compound event is a
combination of two or more simple
events.
The outcome of the first spinner does not
influence the outcome of the second
spinner. The two spins are independent
events.
To find P (A, yellow), find the probability of
each event and multiply.
Step 1. Find each probability.
P (A) = 1/3
P (yellow) = 2/4 = 1/2
Step 2. Multiply.
1/ x 1/ = 1/
3
2
6
The probability of winning a prize is 1/6, or 1
out of 6 tries.
Example 3.
What is the probability of NOT winning a prize in
the spinner game in Example 2?
P (not winning) = 1 - P (winning)
= 1 - 1/6
= 5/6
The probability of not winning is 5/6, or 5 out
of 6 tries.
Example 4.
The letters of the word FLORES were placed
in a bag; find the probability of forming the
word OR if the first letter is put back before
picking the second letter.
Step 1. Find each probability.
P (O) = 1/6
P (R) = 1/6
Step 2. Multiply.
1/ x 1/ = 1/
6
6
36
Example 5.
The letters of the word FLORES were placed
in a bag; find the P (L, E) if the first letter is
NOT put back before picking the second
letter.
Step 1. Find each probability.
P (L- First draw) = 1/6 P (E- Second draw) = 1/5
Step 2. Multiply.
1/ x 1/ = 1/
6
5
30
Moral of the Story
To find the probability of two
independent events, find the probability
of each event and multiply.