Chapter 12 sec 4
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Chapter 12 Sec 4. Multiplying Probability. Independent Events. In situations with two independent events, you can find the probability of both events occurring if you know the probability of each event occurring. Example 1.

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Chapter 12 Sec 4

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Chapter 12 sec 4

Chapter 12 Sec 4

Multiplying Probability


Independent events

Independent Events

  • In situations with two independent events, you can find the probability of both events occurring if you know the probability of each event occurring.


Example 1

Example 1

Sammie Jo has 9 dimes and 7 pennies in her pocket. She randomly selects one coin, looks at it, and replaces it. She then selects another coin. What is the probability that both coins are dimes?

Find the probability of each event. Seeing as both event are independent and the same…

To pull two dimes


Example 2

Example 2

When three dice are rolled, what is the probability that two dice show 5 and the third die shows an even number?


Probability of dependent events

Probability of Dependent Events

  • As with two independent events, you need to find the probability of both events occurring if you know the probability of each event occurring.

  • The second and subsequent events will be affected by each previous event.


Example 11

Example 1

  • Stephen is drawing chips from a bag to determine the prizes to give. Of the 20 chips, 11 say computer, 8 say trip, and 1 says car. Drawing at random and without replacement , find the following probabilities.

  • A computer and a car.

  • Two trips


Chapter 12 sec 5

Chapter 12 Sec 5

Adding Probability


Mutually exclusive events

Mutually Exclusive Events

  • When you roll a die, an event such as rolling a 1 is called a simple eventbecause it consists of only one event.

  • An event that consists of two or more events is a compound event.

  • When the two events not related such as rolling an even number or a 5. Since the roll can not be both the 5 and even, these are called mutually exclusive events.

  • The probability of these events are found by adding their individual probabilities.


Probability of mutually exclusive events

Probability of Mutually Exclusive Events

Jacob has a stack of cards consisting of 10 hearts, 8 spades, and 7 clubs. If he selects a card at random, what is the probability that it is a heart or a club?


Example 21

Example 2

Zoe made a list of 9 comedies and 5 adventure movies she wanted to see. She plans to select 4 titles at random to watch this weekend. What is the probability that at least two of the films selected are comedies?

The term at least implies 2, 3, or 4 films could be comedies. SO, P(2) + P(3) + P(4)


Inclusive events

Inclusive Events

What is the probability of drawing a queen or a diamond from a deck of cards? Since it is possible to draw the queen of diamonds, these events are not mutually exclusive, they areinclusive events.


Example 3

Example 3

There are 2400 subscribers to an Internet service provider. Of these, 1200 own Brand A computers and 500 own Brand B computers, and 100 own both A and B. What is the probability that a subscriber selected at random owns either Brand A or Brand B?


Daily assignment

Daily Assignment

  • Chapter 12 Sections 4 & 5

    • Study Guide (SG)

      • Pg 163 – 166 All

    • CEOC Performance Worksheet


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