Bluman, Chapter 4

Sec 4.5

Probability and Counting Rules

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Bluman, Chapter 4

The counting rules can be combined with the probability rules in this chapter to solvemany types of probability problems.

By using the fundamental counting rule, the permutation rules, and the combination rule, you can compute the probability of outcomes of many experiments, such as getting a full house when 5 cards are dealt or selecting a committee of 3 women and 2 men from a club consisting of 10 women and 10 men.

4.5 Probability and Counting Rules

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Bluman, Chapter 4

Chapter 4Probability and Counting Rules

Section 4-5Example 4-50Page #237

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Bluman, Chapter 4

Four Aces

Find the probability of getting four aces when five cards are drawn from a deck of cards.

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Bluman, Chapter 4

Four Aces

Find the probability of getting four aces when five cards are drawn from a deck of cards.

Make problem simpler!

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Bluman, Chapter 4

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Bluman, Chapter 4

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Bluman, Chapter 4

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Bluman, Chapter 4

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Bluman, Chapter 4

Four of a Kind

Find the probability of getting four of a kind when five cards are drawn from a deck of cards.

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Bluman, Chapter 4

Chapter 4Probability and Counting Rules

Section 4-5Example 4-51Page #238

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Bluman, Chapter 4

Example 4-51

A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities.

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Bluman, Chapter 4

Example 4-51

A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities.

A.) Exactly 2 are defective.

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Bluman, Chapter 4

Example 4-51

A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities.

A.) Exactly 2 are defective. B.) None is defective.

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Bluman, Chapter 4

Example 4-51

A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities.

A.) Exactly 2 are defective. B.) None is defective. C.) All are defective.

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Bluman, Chapter 4

Example 4-51

A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities.

A.) Exactly 2 are defective. B.) None is defective. C.) All are defective. D.) At least 1 is defective.

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Bluman, Chapter 4

Example 4-52: Committee SelectionA store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.

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Bluman, Chapter 4

Example 4-52: Committee SelectionA store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.

TV Graphic: One magazine of the 6 magazines

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Bluman, Chapter 4

Example 4-52: Committee SelectionA store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.

TV Graphic: One magazine of the 6 magazinesNewstime: One magazine of the 8 magazines

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Bluman, Chapter 4

Example 4-52: Committee SelectionA store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.

TV Graphic: One magazine of the 6 magazinesNewstime: One magazine of the 8 magazinesTotal: Two magazines of the 14 magazines

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Bluman, Chapter 4

Example 4-52: Committee SelectionA store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.

TV Graphic: One magazine of the 6 magazinesNewstime: One magazine of the 8 magazinesTotal: Two magazines of the 14 magazines

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Bluman, Chapter 4

Example 4-52: Committee SelectionA store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased.

TV Graphic: One magazine of the 6 magazinesNewstime: One magazine of the 8 magazinesTotal: Two magazines of the 14 magazines

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Bluman, Chapter 4

Chapter 4Probability and Counting Rules

Section 4-5Example 4-52Page #238

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Bluman, Chapter 4

Chapter 4Probability and Counting Rules

Section 4-5Example 4-53Page #239

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Bluman, Chapter 4

Example 4-53: Combination LocksA combination lock consists of the 26 letters of the alphabet. If a 3-letter combination is needed, find the probability that the combination will consist of the letters ABC in that order. The same letter can be used more than once. (Note: A combination lock is really apermutation lock.)

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Bluman, Chapter 4

Example 4-53: Combination LocksA combination lock consists of the 26 letters of the alphabet. If a 3-letter combination is needed, find the probability that the combination will consist of the letters ABC in that order. The same letter can be used more than once. (Note: A combination lock is really apermutation lock.)

There are 26·26·26 = 17,576 possible combinations.

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Bluman, Chapter 4

Example 4-53: Combination LocksA combination lock consists of the 26 letters of the alphabet. If a 3-letter combination is needed, find the probability that the combination will consist of the letters ABC in that order. The same letter can be used more than once. (Note: A combination lock is really apermutation lock.)

There are 26·26·26 = 17,576 possible combinations.The letters ABC in order create one combination.

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Bluman, Chapter 4

Example 4-53: Combination LocksA combination lock consists of the 26 letters of the alphabet. If a 3-letter combination is needed, find the probability that the combination will consist of the letters ABC in that order. The same letter can be used more than once. (Note: A combination lock is really apermutation lock.)

There are 26·26·26 = 17,576 possible combinations.The letters ABC in order create one combination.

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Bluman, Chapter 4

On your own:

Read “Speaking of Statistics” on page 240

Sec 4-5 page 240 Exercises #1-17

odds

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