52 ch13probability2007

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1) Mendel's laws of segregation and independent assortment reflect the same laws of probability that govern coin tosses and dice rolls. 2) Calculating the probability of producing a particular gamete is analogous to calculating the probability of a coin toss, with a 50% chance either way. 3) The probability of outcomes from genetic crosses can be calculated using the rules of multiplication and addition, just as with probability calculations for coin tosses and other independent events.

Probability & Genetics

AP Biology

2006-2007

Genetics & Probability
 Mendel’s laws:
segregation
 independent assortment


reflect same laws of
probability that apply to
tossing coins or rolling dice

AP Biology

Probability & genetics
 Calculating probability of
making a specific gamete
is just like calculating the
probability in flipping a
coin
probability of tossing
heads?
 probability making a B
gamete?

B
100%

BB
B



AP Biology

B
50%

Bb
b

Probability & genetics
 Outcome of 1 toss has no
impact on the outcome of the
next toss
probability of tossing heads
each time? 50%
 probability making a B gamete
each time? 50%


B

Bb
b
AP Biology

Calculating probability
Pp x Pp

P

p

egg

offspring

P

male / sperm

sperm

P

PP

P

p

p

P

1/2 x 1/2

female / eggs

1/2 x 1/2

P

PP

Pp

p

Pp

pp

AP Biology

1/2 x 1/2

p

p

1/2 x 1/2

=
=
=

=

1/4

Pp

1/4
+
1/4
1/2

pp

1/4

Rule of multiplication
 Chance that 2 or more independent
events will occur together


probability that 2 coins tossed at the
same time will land heads up

1/2 x 1/2 = 1/4


probability of Pp x Pp → pp

1/2 x 1/2 = 1/4
AP Biology

P
Pp
p

Calculating probability in crosses
Use rule of multiplication to predict crosses

YyRr x YyRr

x

Yy

Yy

Rr

yyrr

x

?%
1/16
yy
AP Biology

rr
1/4

x

1/4

Rr

Apply the Rule of Multiplication
AABbccDdEEFf

x

AaBbccDdeeFf

AabbccDdEeFF

Got it?
Try this!

AP Biology

AA x Aa → Aa
Bb x Bb → bb
cc x cc → cc
Dd x Dd → Dd
EE x ee → Ee
Ff x Ff → FF

1/2
1/4
1
1/2
1
1/4

1/64

Rule of addition
 Chance that an event can occur
2 or more different ways
 sum of the separate probabilities
 probability of Bb x Bb → Bb
sperm

egg

offspring

B

b

Bb

1/2 x 1/2 =

b

B

1/2 x 1/2 =
AP Biology

1/4

Bb

1/4

1/4
+ 1/4
1/2

Chi-square test
 Test to see if your data supports


your hypothesis
Compare “observed” vs. “expected” data
is variance from expected due to
“random chance”?
 or is there another factor influencing data?


 null hypothesis
 degrees of freedom
 statistical significance

AP Biology

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52 ch13probability2007

1. Probability & Genetics AP Biology 2006-2007

2. Genetics & Probability  Mendel’s laws: segregation  independent assortment  reflect same laws of probability that apply to tossing coins or rolling dice AP Biology

3. Probability & genetics  Calculating probability of making a specific gamete is just like calculating the probability in flipping a coin probability of tossing heads?  probability making a B gamete? B 100% BB B  AP Biology B 50% Bb b

4. Probability & genetics  Outcome of 1 toss has no impact on the outcome of the next toss probability of tossing heads each time? 50%  probability making a B gamete each time? 50%  B Bb b AP Biology

5. Calculating probability Pp x Pp P p egg offspring P male / sperm sperm P PP P p p P 1/2 x 1/2 female / eggs 1/2 x 1/2 P PP Pp p Pp pp AP Biology 1/2 x 1/2 p p 1/2 x 1/2 = = = = 1/4 Pp 1/4 + 1/4 1/2 pp 1/4

6. Rule of multiplication  Chance that 2 or more independent events will occur together  probability that 2 coins tossed at the same time will land heads up 1/2 x 1/2 = 1/4  probability of Pp x Pp → pp 1/2 x 1/2 = 1/4 AP Biology P Pp p

7. Calculating probability in crosses Use rule of multiplication to predict crosses YyRr x YyRr x Yy Yy Rr yyrr x ?% 1/16 yy AP Biology rr 1/4 x 1/4 Rr

8. Apply the Rule of Multiplication AABbccDdEEFf x AaBbccDdeeFf AabbccDdEeFF Got it? Try this! AP Biology AA x Aa → Aa Bb x Bb → bb cc x cc → cc Dd x Dd → Dd EE x ee → Ee Ff x Ff → FF 1/2 1/4 1 1/2 1 1/4 1/64

9. Rule of addition  Chance that an event can occur 2 or more different ways  sum of the separate probabilities  probability of Bb x Bb → Bb sperm egg offspring B b Bb 1/2 x 1/2 = b B 1/2 x 1/2 = AP Biology 1/4 Bb 1/4 1/4 + 1/4 1/2

10. Chi-square test  Test to see if your data supports  your hypothesis Compare “observed” vs. “expected” data is variance from expected due to “random chance”?  or is there another factor influencing data?   null hypothesis  degrees of freedom  statistical significance AP Biology

11. AP Biology

12. Any Questions?? AP Biology 2006-2007

52 ch13probability2007

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