Transcript OR 1/2 + 1/2 + 1/2 + 1/2

Chapter 14.
Probability & Genetics
https://www.youtube.com/watch?v=y4Ne9DXk_Jc
Genetics & Probability
 Mendel’s laws:
Segregation
 Dominance
 Independent Assortment

reflect same laws of
probability that apply to
tossing coins or rolling dice
Probability & genetics
 Calculating probability of
making a specific gamete
is just like calculating the
probability in flipping a
coin
probability of tossing
heads? 50% or 1/2
 probability making a P
gamete…
H
50%
Hh
h

PP
P
100%
P
Probability & genetics
 Outcome of 1 toss has no
impact on the outcome of the
next toss = independent events
probability of tossing heads
each time? 50%
 probability making a P gamete
each time? 50%

P
Pp
p
Calculating probability
Pp x Pp
female / eggs
P
PP
p
Pp
egg
offspring
P
P
PP
P
p
1/2 x 1/2 =
male / sperm
P
sperm
Chance that an
event can occur
in 2 or more
different ways =
Rule of Addition
Pp
pp
Pp
1/2 x 1/2 =
p
P
1/2 x 1/2 =
p
1/4
1/4
+
1/4
1/2
p
p
1/2 x 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
Calculating dihybrid probability
 Rule of multiplication also applies to
dihybrid crosses
heterozygous parents — YyRr
 probability of producing a yyrr offspring?

 probability of producing y gamete =
1/2
 probability of producing r gamete =
1/2
 probability of producing yr gamete =
1/2 x 1/2 = 1/4
ie. An ovum
 probability of producing a yyrr offspring =
1/4 x 1/4 = 1/16
ie. An ovum & a sperm
Rule of addition
to determine the chances of heterozygous possibilities
 Chance that an event can occur
2 or more different ways
 sum of the separate probabilities
 probability of Pp x Pp  Pp
sperm
egg
offspring
P
p
Pp
1/2 x 1/2 =
p
P
1/2 x 1/2 =
1/4
pP
1/4
1/4
+ 1/4
1/2
Rule of
Multiplication
Independent events in sequence
1/2 x 1/2 x 1/2 x 1/2 =
X
AND
(and then)
Rule of
Addition
Mutually exclusive events
1/2 + 1/2 + 1/2 + 1/2 =
+
OR
Probability Examples
1. What are the chances of having 4 boys and then a girl?
2. A couple has 2 children, both girls. If the woman gives
birth to a third child, what is the probability that the third
child will be a boy?
3. What’s the probability that the genotype Bb will be
produced from parents Bb x Bb?
4. What’s the probability that the genotype ttgg will be
produced by parents TtGg x TtGg?
5. What’s the probability that the genotype Aa will be
produced by parents aa x Aa?
Probability Examples
6. A student has a penny, nickel, dime, and a quarter. She flips them all
simultaneously and checks for heads or tails. What is the probability that all
four coins will come up heads? She flips all four coins again. What is the
probability she well get four heads both times?
What probability rule did you use to determine this?
7. Using Hardy-Weinberg’s Equation of Equilibrium: p2 + 2pq + q2
What is the probability of expressing the dominant phenotype?
8. What is the chance that a child will carry the HbS gene but not have
sickle cell disease?
9. What are the chances that two heterozygous parents for sickle cell will have
three children who are homozygous for normal RBS’s?
10. Assume a germ cell has HhEe, where h and e are each on a single gene and
the genes are not linked. What is the probability of a gamete having he?
What is the probability of having a blond(e) hair, blue-eyed baby if both
parents are dihybrids?
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”?
is there another factor influencing data?
 degrees of freedom (df) = # of classes -1 = (n-1)
 statistical significance - unlikely to have occurred by chance
 null hypothesis - one you can accept or reject based on probability
X2 = ∑ (Observed Value - Expected Value) 2
Expected Value