Probability & Genetics
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
 Each toss is independent, just
like the distribution of alleles
into gametes
probability of tossing heads
each time?
50%
Bb
 probability making a B gamete
each time?
50%

AP Biology
B
b
Probability & genetics
 Like a coin toss,
each ovum from a
heterozygous parent
has ½ a change of
carrying the
dominant allele and
½ chance of carrying
the recessive allele
 The same odds
apply to sperm
AP Biology
Calculating probability
Pp x Pp
sperm
egg
offspring
P
P
PP
P
p
1/2 x 1/2
=
1/4
male / sperm
P
p
female / eggs
1/2 x 1/2
P
PP
Pp
p
Pp
pp
p
=
p
1/2 x 1/2
AP Biology
=
P
1/2 x 1/2
p
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
P
Pp
p
AP Biology
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
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
Rule of addition
 Example: There are 2 ways that
gametes can combine to form a
heterozygote
The dominant allele could come from
sperm and recessive allele from egg
(probability = ¼)
 Or the dominant allele could come from
egg and recessive from sperm
(probability = ¼)
 The probability to a heterozygote is ¼ +
¼=½
AP Biology

 The probability of producing a ppyyRr offspring:
The probability of producing pp = 1/2 x 1/2 = 1/4.
 The probability of producing yy = 1/2 x 1 = 1/2.
 The probability of producing Rr = 1/2 x 1 = 1/2.
 Therefore, the probability of all three being present
(ppyyRr) in one offspring is 1/4 x 1/2 x 1/2 = 1/16.
For ppYyrr: 1/4 x 1/2 x 1/2 = 1/16.
For Ppyyrr: 1/2 x 1/2 x 1/2 = 2/16
For PPyyrr: 1/4 x 1/2 x 1/2 = 1/16
For ppyyrr: 1/4 x 1/2 x 1/2 = 1/16
Therefore, the chance of at least two recessive traits is
6/16.






AP Biology