Warm up

1) What is the theoretical probability of rolling the sum of 3 on two dice?

2) What is the experimental probability of each color if you rolled a die 25 times and landed on red 8 times and blue 12 times and green 5 times?

3) If we select 2 cards from a standard 52 card deck. What is the probability that both are face cards?

© 2010 Pearson Education, Inc. All rights reserved. Section 14.1, Slide 2

Probability and Genetics

Y – produces yellow seeds (dominant gene) g – produces green seeds (recessive gene)

© 2010 Pearson Education, Inc. All rights reserved. Section 14.1, Slide 3

Probability and Genetics

Crossing two first generation plants:

Punnett Square

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• Example: Sickle-cell anemia is a serious inherited disease. A person with two sickle-cell genes will have the disease, but a person with only one sickle-cell gene will be a carrier of the disease. If two parents who are carriers of sickle-cell anemia have a child, what isthe probability of each of the following:

Probability and Genetics

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a) The child has sickle-cell anemia?b) The child is a carrier?c) The child is disease free?

© 2010 Pearson Education, Inc. All rights reserved. Section 14.1, Slide 5

• Solution: Use a Punnett square:s denotes sickle cell n denotes normal cell.

Probability and Genetics

© 2010 Pearson Education, Inc. All rights reserved. Section 14.1, Slide 6

• Solution: Use a Punnett square:s denotes sickle cell n denotes normal cell.

Probability and Genetics

© 2010 Pearson Education, Inc. All rights reserved. Section 14.1, Slide 7

Odds

If a family has 3 children, what are the odds against all 3 children being of the same gender?

What are the odds in favor?

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Odds

If a family has 3 children, what are the odds against all 3 children being of the same gender? 6:2 or 3:1

What are the odds in favor? 1:3

© 2010 Pearson Education, Inc. All rights reserved. Section 14.1, Slide 9

Odds• Example: A roulette wheel has 38 equal-size compartments. Thirty-six of the compartments are numbered 1 to 36 with half of them colored red and the other half black. The remaining 2 compartments are green and numbered 0 and 00. A small ball is placed on the spinning wheel and when the wheel stops, the ball rests in one of the compartments. What are the odds against the ball landing on red?

(continued on next slide)

© 2010 Pearson Education, Inc. All rights reserved. Section 14.1, Slide 10

Odds• Solution:

There are 38 equally likely outcomes. 18 are in favor of the event “the ball lands on red” and 20 are against the event.

The odds against red are 20 to 18 or 20:18, which we reduce to 10:9.

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Odds

If the probability of E is 0.3, then the odds against E are

We may write this as 70:30 or 7:3.

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Odds• Example: If the probability of Green Bay winning the Super Bowl is 0.35. What are the odds against Green Bay winning the Super Bowl?

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Odds• Example: If the probability of Green Bay winning the Super Bowl is 0.35. What are the odds against Green Bay winning the Super Bowl?• Solution: From the diagram we compute

That is, the odds against are 13 to 7.