Transcript 14.1 cont notes

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?
Probability and Genetics
Y – produces yellow seeds (dominant gene)
g – produces green seeds (recessive gene)
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Section 14.1, Slide 2
Probability and Genetics
Crossing two first
generation plants:
Punnett Square
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Section 14.1, Slide 3
Probability and Genetics
• 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 sicklecell anemia have a child, what is
the probability of each of the following:
a) The child has sickle-cell anemia?
b) The child is a carrier?
c) The child is disease free?
(continued on next slide)
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Section 14.1, Slide 4
Probability and Genetics
• Solution:
Use a Punnett square:
s denotes sickle cell
n denotes normal cell.
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Section 14.1, Slide 5
Probability and Genetics
• Solution:
Use a Punnett square:
s denotes sickle cell
n denotes normal cell.
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Section 14.1, Slide 6
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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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? 6:2 or 3:1
What are the odds in
favor? 1:3
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Section 14.1, Slide 8
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)
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Section 14.1, Slide 9
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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Section 14.1, Slide 10
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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Section 14.1, Slide 11
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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Section 14.1, Slide 12
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.
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Section 14.1, Slide 13