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**Ch 11 – Probability & Statistics**

11.3 – Independent and Dependent Events

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**Probability of Independent Events**

Events are independent events if the occurrence of one event does not affect the probability of the other. Probability of Independent Events If A and B are independent events, then

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A six-sided number cube is labeled with the numbers 1, 2, 2, 3, 3, and 3. Four sides are colored red, one side is white, and one side is yellow. Find each probability. Tossing 2, then 2 B. Tossing red, then white, then yellow

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**Probability of Dependent Events**

Events are dependent events if the occurrence of one event affect the probability of the other. To find the probability of dependent events, you can use conditional probability P(B|A), the probability of event B, given that event A has already occurred. Probability of Dependent Events If A and B are dependent events, then

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**Two number cubes are rolled—one blue and one yellow**

Two number cubes are rolled—one blue and one yellow. Explain why the events are dependent. Then find the indicated probability. 1 2 3 4 5 6 The blue cube shows a 6 and the sum is greater than 9. The yellow cube shows an even number and the sum is 5.

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**Domestic Migration by Region**

The table shows domestic migration from 1995 to A person is randomly selected. Find each probability. Domestic Migration by Region (thousands) Region Immigrants Emigrants Northeast 1537 2808 Midwest 2410 2951 South 5042 3243 West 2666 2654 That an emigrant is from the West That someone selected from the South is an immigrant That someone selected is an emigrant and is from the Midwest

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**What do you know about face cards?**

52 Cards Total 2 Colors Red 26 cards Black 26 cards 4 Suits Hearts ♥ Red 13 cards Diamonds ♦ Red 13 cards Clubs ♣ Black 13 cards Spades ♠ Black 13 cards 4 cards of each Number Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King

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Replacement? Two cards are drawn from a deck of 52. Determine whether the events are independent or dependent. Find the probability. Selecting two hearts when the first card is replaced Selecting two hearts when the first card is not replaced A queen is drawn, is not replaced, and then a king is drawn

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Probability of Independent Events

Probability of Independent Events

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