The Multiplication Rule of Probability

Multiplication Rule

​This rule pertains to multiple, combined probabilities (probabilistic circumstances) that are

INDEPENDENT

of each other.

Poll

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

• Dependent

• Independent

Dependent vs Independent

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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: Going to school today

Event B: Going to school tomorrow

• 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

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Example 1: 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.

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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. [Round your answer to three decimal places.]

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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 all of them are acceptable. [Write your answer as a decimal rounded to three decimal places.]

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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.]

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A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from from the bin and placed back in after identification, find the probability that all the bulbs selected are good ones. [Write your answer as a decimal rounded to three decimal places.]

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Example 2: Find the probability of randomly selecting two even numbered tiles without replacement. [Write your answer as a decimal rounded to three decimal places.] In other words, after you 'pluck' out your choice tile, it is NOT replaced back into the pile from which to be chosen (2nd trial will have 7 tiles).

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You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. [Write your answer as a decimal rounded to three decimal places.]

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A IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the probability that she selects none of those containing errors? [Write your answer as a decimal rounded to three decimal places.]

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Among the contestants in a competition are 46 women and 23 men. If 5 winners are randomly selected, what is the probability that they are all men?

(Remember - when you have a discrete sample size, assume you will be 'plucking' out your events and creating a new event based on your previous event... If the question STATES that an item is replaced or put back, then you will go with the independent model)

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Multiple Choice

Two different people are randomly selected from the 991 subjects, find the probability that they are both heavy smokers.

Dependent or independent?

• Dependent

• Independent

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If two different people are randomly selected from the 991 subjects, find the probability that they are both heavy smokers. [Write your answer as a decimal rounded to three decimal places.]

Multiple Choice

Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 6 possible answers.

Dependent or Independent?

• Dependent

• Independent

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Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 6 possible answers. [Write your answer as a fraction.]

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