The Multiplication Rule of Probability

Probability "and" Review

Objective: Students will be able to use the multiplication rule to find probabilities that are independent of each other.

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Reminder:
Dependent vs Independent

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Poll

You flip a coin twice. Is the probability of the second flip DEPENDENT or INDEPENDENT of the first flip?

• Dependent

• Independent

Multiple Choice

Are the two events dependent or independent?

Event A: rolling a die

Event B: rolling a die again

• Dependent

• Independent

Multiple Choice

Are the two events dependent or independent?

Event A: Passing to the 11th grade

Event B: Passing to the 12th grade

• Dependent

• Independent

Finding "And" probabiltiy

Multiplication Rule

If you have two or more events that are INDEPENDENT to find the probability of both happening you MULTIPLY their probabilities together.

Example #1

There is a 42% chance that the workers at a company will guess the next client correctly.
What is the probability that the workers guess the next three clients correctly?

Example #1

There is a 42% chance that the workers at a company will guess the next client correctly.
What is the probability that the workers guess the next three clients correctly?

__0.42__ x __0.42__ x __0.42__ = 0.074
Client#1 Client #2 Client #3

There is a 0.074 or 7.4% chance that the workers will be correct the next three times.

Example #2

There is a 42% chance that the workers at a company will guess the next client correctly.
What is the probability if the workers guess the next three clients, the first one will be correct and the final two will be incorrect?

Example #2

There is a 42% chance that the workers at a company will guess the next client correctly.
What is the probability if the workers guess the next three clients, the first one will be correct and the final two will be incorrect?

__0.42__ x __0.58__ x __0.58__ = 0.141
Client#1 Client #2 Client #3

There is a 0.141 or 14.1% chance that the workers will be correct and then incorrect twice over the next three clients.

Fill in the Blank

Find the probability that a woman gives birth to two children and both are boys.

Write your answer as a decimal rounded to three decimal places.

Hint: The probability of having a girl/boy = 0.5

Fill in the Blank

In one town, 44% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats.

Write your answer as a decimal rounded to three decimal places.

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Fill in the Blank

In one town, 44% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that one is a Democrat and one is not a Democrat.

Write your answer as a decimal rounded to three decimal places.

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Fill in the Blank

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that the first 2 are acceptable and that last is defective.

Write your answer as a decimal rounded to three decimal places.

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Fill in the Blank

A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.

Write your answer as a decimal rounded to three decimal places.

Fill in the Blank

A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones?

Write your answer as a decimal rounded to three decimal places.