independent events lesson 11-7 pg. # 432-433. ca content standards statistics, data analysis, and...
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Vocabulary: COMPOUND EVENT An event that is a combination of two or more single events.TRANSCRIPT
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Independent Events
Lesson 11-7Lesson 11-7Pg. # 432-433Pg. # 432-433
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CA Content StandardsStatistics, 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.
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Vocabulary: COMPOUND EVENT
An event that is a combination of two or more single events.
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Vocabulary: INDEPENDENT EVENTSTwo events in which the outcome of the second is not affected by the outcome of the first.
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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.
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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)?
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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).
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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
C
B
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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.
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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.1/3 x 1/2 = 1/6
The probability of winning a prize is 1/6, or 1 out of 6 tries.
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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.
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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.1/6 x 1/6 = 1/36
Example 4.
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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.1/6 x 1/5 = 1/30
Example 5.
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Moral of the Story
To find the probability of two independent events, find the probability of each event and multiply.