Transcript ADVANCED GENETICS

COMPLEX PROBABILITIES AND
ADVANCED GENETICS
BEGINS
Hi there and welcome to the
newest, hottest game-show in
town! Welcome to What’s the
Probability!. Now lets have a
round of applause for our host,
Mr. Chance
Welcome to the show. Tonight our show
will feature contestants from
Leamington Ontario, the Tomato capital!
They are the Cardinal Carter Catholic
Cougars!
Go...........COUGARS!
In this game of risk, we start
with $100 questions. Once
you pass a showcase ,the
stakes go up and questions
are worth ten times as
much. Each subsequent
showcase you pass results in
another ten times increase
in money per correct
question. But remember,
once you get a question
wrong, you lose all the cash
and you are out of the
game.
For our first round, each question is worth $ 100. If, however, you
get one question wrong you lose all the money and the game.
Here is your first question. If the genotype of a man is Tt, what is
the probability of the sperm being t?
The probability is 1/2
T
1 out of 2
eggs are “t”
t
sperm1
Sperm 2
This is like flipping a coin.
The prob. of getting a T is
½ or a t is 1/2
A woman has the genotype AaTt. What is the
probability of the egg being AT
$200
$100
$0
The probability is 1/4
The probability of
getting the A is ½. The
probability of getting the
t is ½. Multiply them to
get the prob. Together.
AT
At
½ x ½ = 1/4
aT
at
Same result
1 out of 4
eggs is AT
Okay CC cougar, tell me this. If a man is TtAaBb, what is the
probability his sperm will be tAb?
Probability of t is ½.
Probability of A is ½.
Probability of b is ½
Total ½ x ½ x ½ = 1/8
The probability of tAb in the sperm is 1/8
$200
$400
$300
You are doing great Cougars! What is a woman has the genotype
TTaaBb. What is the probability of her eggs being TaB?
Probability of T is 1.
Probability of a is 1.
Probability of B is ½
Total 1 x 1 x ½ = 1/2
You are using the
multiplication rule in
these questions!!
The probability of the TaB egg is ½.
How many different gametes can an organism
with DdEeTt produce?
You are
correct!
$500
$400
Each sex cell will have 3 letters in
this situation. Ex DET
We just need to know how
many different combinations
are possible.
8 different combinations are possible.
If you tried to do a trihybrid cross the
punnett would be 8 x 8 with 64
squares. That’s just too big!
You mean
DET like
Detroit 8 mile
uh hu.
You are doing very well. Lets change the questions a little.
Now instead of dealing in sperm or egg, let’s deal with the
probabilities of particular offspring. A man is genotype Aa
and a woman is genotype Aa. What is the probability of
them having a Aa child?
$600
$500
A
Aa
A
a
a
aA
Punnet prob.
of Aa is 1/2
same
Since this deals with a diploid organism, it has a new rule—the
ADDITION – rule.
If you have an AA or aa don’t worry, use the same technique
with the multiplication rule.
Only if you have an Aa crossed to another Aa , two
heterozygotes, does the ADDITION rule get added in.
First use the multiplication rule.
Probability of Aa is ½ x ½ = ¼
Probability of aA is ½ x ½ - ¼
It relates that you can get the A from the dad and the a from
the mom –prob. ¼ or you can get the a from the dad and A
from the mom – prob 1/4. You have to add those two
probabilties to get the probability of the heterozygote offspring
Aa. Thus ADDITION RULE now ¼ + ¼ = 1/2
The probability of getting Aa in the offspring is 1/2
Wait a minute. You lost me with all them”
thar” addition rules. I don’t understand
that “thar” stuff!
Well if you are having difficulty with the math (dont’t worry,
most people seem to have this problem) You can get the right
answer by simply using 4 box punnett squares to calculate each
probability.
Break up the
problem. Start with
HH x Hh
H
H
H
h
HH
Hh
HH
Hh
For example, determine the probability of
HhRr x HHRr having a HHRr offspring
Probability
of HH is
1/2
Now combine the
probabilities to get the
overall answer.
HH
½
Rr
x
½ = 1/4
Chance of HhRr x HHRr having HHRr is 1/4
Probability
of Rr x Rr
R
R
r
r
Rr
RR
Rr
rr
Probability
of Rr is 1/2
Hey I kinda understand that.
Try another one. Determine the
probability of YyTt x YyTt having a yytt
offspring.
Break up the
problem. Start with
Yy x Yy
Y
y
Y
YY
Yy
y
Yy
yy
Probability
of yy is 1/4
Probability
of Tt xTtr
Now combine the
probabilities to get the
overall answer.
yy
1/4
tt
T
t
T
TT
Tt
t
Tt
tt
x 1/4 = 1/16
Chance of YyTtr x YyTt having yytt is
1/16
If you remember your punnett square
work, this is the end result of the 16
box dihybrid cross probability.
Probability of
tt is 1/4
We have now arrived at the $hundred dollar showcase. So far in the
game you have accumulated $600, You can either continue playing and
risk losing the money if you answer any question wrong, or you can buy
and keep a showcase right now that is behind one of those curtains.
Remember, the decision is yours, its all about probability!!
I choose showcase #3
$600
$0
Well okay then. But first, let’s see what
you didn’t pick.
1
You would have got a
roan cow. Got milk?
2
You would have got a
breeding pair of
Andalusian Fowl.
3
You have won a trip to
fabulous Vienna Austria!!
You
will visit Mendel’s original pea garden
Okay, now it’s time for your CHALLENGE questions. Each
question is worth $1000 If a man TTHh is married to a
woman TtHH, what is the probability that they will have a
TtHh child?
TT x Tt to produce Tt is ½
..see slide before
showcase if you need to
see the punnett
$1000
$0
Correct. You
are really on a
roll now! I
think it’s time
for something
more difficult.
Hh x HH to produce Hh is
½.. Look three slides back
if you need to see punnett
Now combine the probabilities
to get the overall answer.
Tt
½ $200x
Hh
½ = 1/4
Chance of TtHh x TtHh having yytt is 1/4
The probability is 1/4
If a man YyRrHh is married to a woman YyRrHH, what is the
probability that they will have a yyRrHH child?
Yy x Yy to produce yy is
1/4 ..see 4 slides back if
you need to see the
punnett
$2000
$1000
Correct. You
know how to
determine
probabilities
on the tricross
questions.
Awesome!
Rr x Rr toproduce
Rr is ½. Look
three slides back
if you need to ..
Hh x HH to produce HH
is ½.. Look three slides
back if you need to see
punnett
Now combine the probabilities
to get the overall answer.
yy
Rr
¼
x ½ x
Hh
½ = 1/16
Chance of YyRrHh x YyRrHH having yyRrHH
is 1/16
The probability is 1/16
In the four o’clock flower red and white flowers are
incompletely dominant and produce pink. Tall is dominant to
dwarf. Two heterozygous tall pink flower plants are mated.
What is the probability of getting dwarf pink flowers?
Dwarf pink flowers is ttRr
TtRr x TtRr
$3000
$2000
Tt x Tt to produce
tt is 1/4
tt
¼
Rr x Rr to
produce Rr is 1/2
Rr
x
1/2
= 1/8
The probability is 1/8 of having the dwarf pink flowers
Hemophilia is sex linked and recessive on the X
chromosome. Two parents are not hemophiliac.
They both had hemophiliac fathers. What is the
probability that their first child will be hemophiliac?
A woman with a hemophiliac dad
must be a carrier of hemophilia
Mother
is carrier
X HX h
x
X HY
X linked is passed from carrier
mother to afflicted son.
XH
Xh
Male is normal
XH
XH
Y
$3000
$4000
Hemophiliac dad
X HX h X HY
X HX h X HY
Y
XH
X HX H X HY
Xh
X HX h X hY
All females
are
carriers
Chances are ¼ to have hemophiliac child
Good
response.
The Y is dominant yellow and R is dominant round.
Recessive y is green and r recessive wrinkled. In the
cross YyRr x YyRr, determine the proportion of Yellow
and round individuals that are pure breeding
( homozygous at both alleles)
Translation: YyRr x YyRr probabiliy to produce YYRR
$5000
$4000
Yy x Yy to produce
YY is 1/4 ..
Very
good!
¼
Rr x Rr to produce
RR is 1/4 ..
x
¼=
1/16
Proportion of individuals is 1/16
In the Bat normal wings N are autosomal dominant to short n wings.
Two normal wing carriers of short wing are mated and produce a
short wing offspring. What it the probability of them having the
second offspring shortl also?
N
$6000
$5000
N
n
Correct
again!
n
NN
Nn
Nn
nn
Probabilities of each event
remain independent. Just like
a coin flip. You cannot tell how
it will flip from the previous
flip.
¼ Prob of
vestigial
Probability of second bat also being
short wing is still 1/4
In the mammals, the sex ratio is approximately 1 boy
to 1 girl . Is this by accident or are genetics at work?
X
$8000
$7000
$6000
Y
X
XX
XY
X
XX
XY
From the punnett square, you
can see it is no accident. All
matings between male and
female result in a 50/50 ratio as
shown by the punnett.
What is the probability of a family having 4 successive births of male
babies in a row ?
½ x ½ x ½ x ½ = 1/32
Probability of 5 boys in a row is 1/32
Two parents both TtRr mate. T is dominant T and t is
recessive short. R is dominant red fur and r is recessive white
fur. What is the probability that the offspring will express
both the dominant phenotype of the first allele and the
recessive phenotype of the second allele?
Identify the offspring that the
question is talking about first!
Situation 1 TTrr
Or
Situation 2 Ttrr
$8000
$9000
Correct
Situation 1
Tt x Tt to
produce TT is ¼
¼ x ¼ = 1/16
Situation 2
Rr x Rr to
produce rr is ¼
Tt x Tt to
produce Tt is ½
Add these
1/16 + 2/16 = 3/16
Rr x Rr to
produce rr is ¼
½ x ¼ = 1/8
The probability is 3/16
During meiosis one plant ovum does not reduce the chromosomes
and is pollinated. This results in a type of polyploidy. What is a
possible chromosome number for the hybrid if the normal plant
chromosome number is 10?
Now just a cotton pickin minute thar. I’m aware of haploid
and diploid but what is this polypoid about?
$9000
Polyploid is a chromosomal alteration in which the organism
possesses more than two complete chromosome sets. It is primarily
limited to plant hybridizations but some rare animals have been
identified as tetraploid. Examples are 3n triploidy and 4n tetraploidy.
The burrowing rodent species , Tympanoctomys barrerae
is tetrapoid to a closely related species. Polypoidy in
animals. The full set of extra chromosomes has little
adverse effect, unlike problems aminals have with one
single extra chromosome such as Down’s syndrome.
We’re waiting for your answer.
Pollen would be haploid –
thus 5 chromosomes
Ovum is diploid – thus
10 chromosomes
The chromosome number of the diploid individual would be 15.
Yes it is. Subsequent attempts for this 15
chromosome to divide into a haploid
gamete are not even possible. Is it 7 or 8
that you use as the haploid number? Thus
the hybrid is sterile, definitely being unable
to chromosome pair with the original
species that has pollen and ova with 5
chromosomes. .
$10000
$9000
Correct
again, but is
it infertile as
a result?
I’m sorry but you’ve made an error. You’ve lost all the money.
That’s too bad and you would have made it to the fabulous
thousand dollar showcase had your answer been correct.
Here is the correct answer. The organism is not sterile. It is
true that is cannot interbreed with the originating species,
however, it can interbreed with another plant which has 5
haploid chromosomes. This could generate a 20
chromosome organism. This is called ALLOPLOID and these
individuals are actually a new species. This is important in
plant evolution. Plants are crazy about this process, so be
careful if you ever get another question on this
$10000
$0
That’s all we have for today.
Thanks for joining us folks. See you
next week when our topic will be
Probability and the World Series of
Poker.
CALLING ALL YOU MATH EXPERTS. THIS IS ESPECIALLY RELEVANT IF
YOU ARE TAKING THE DATA ANALYSIS CLASS. YOU CAN ADD THIS TO
ONE OF YOUR DISCUSSIONS. Is the WHAT’S THE PROBABILITY gameshow scenario feasible. Other shows like WHO WANTS TO BE A
MILLIONAIRE and DEAL OR NO DEAL are carefully crafted to play a
game of odds and risk. These game-shows offer great rewards, but
do they really pay out? How would you rate WHAT’S THE
PROBABILITY? and explain why. Hand it in as a bonus assignment!
It might even be good for your math teacher too.
COMPLEX PROBABILITIES AND
ADVANCED GENETICS
ENDS