Let us use these probabilities to now try
and predict outcomes of perhaps a monohybrid
cross to see how it applies to genetics. Trust
me it is really much more simple than you
think. The probability of having a homozygous
recessive outcome from a heterozygous self
cross, we know by looking at our favourite
Punnett square that is a 1/4th probability.
Homozygous recessive, the white flower is
a 1/4th probability. Let us look at it mathematically.
If we look at the male parent up on the top,
we see that he could contribute a big P or
a small p. The pollen could be P or p and
then if we look at the female parent, it could
also contribute a P or a p. Each of those
have a 1/2 probability. You are either going
to get P or you are going to get p. We can
say what we need in order to get the
white flower is a p from the parent
and a p from the other parent. We need to
have two pps in which case we have an AND
problem. Most genetics problems will truly
use the AND rule. Here we have a 1/4 chance
mathametically. We have shown that we do indeed
have a 1/4 chance of getting the homozygous
recessive white flower.
Hopefully you are beginning to trust that
these methods of calculating probabilites
are slightly easier than or at least faster
than drawing a Punnett square. You can play
with this using coins and saying I have 10
coins and I have a 50 percent chance of heads
or tails and if I have 10 coins, you know
you can throw them 1000s of times, but you
could trust based on a knowledge of Punnett
square that they do work out.
Now let us look at the probability in the
same cross of getting a heterozygote. In this
case, purple, but heterozygously purple. There
are two ways to get that heterozygote purple.
One is by the male parent contributing a little
p and the female parent contributing a P.
The other is by the female parent contributing
a p and the male parent contributing a P.
We know from our knowledge of Punnett squares
and our knowledge of these heterozygote crosses,
we already know there is a 50 percent probability
and there is a 1/4 probability of each different
ways. We can add those two probabilities together
in order to find out that yes indeed 50 percent
or 1/2 of the progeny from this cross will
end up being heterozygous, but there are two
different ways to become heterozygous, so
you could become heterzygous by this way or
this way. Hopefully, we can trust these rules
and you can transition into using them to
calculate the outcomes of crosses. An example
of where you might need this is perhaps if
you were doing a trihybrid or a tetrahybrid
cross. Could you imagine making the Punnett
square from that? You would be working for
hours trying to keep track of all the different
gametes and finally have an outcome and try
to keep track of all of the different genotypes.
Trust me. The probability method is much simpler.
Let us use it to take care of a dihybrid cross
with probabilities. We have already explored
monohybrid, but we can make a dihybrid cross
much more simple. Let us say, we split the
two traits. We are looking at round versus
wrinkled, the r allele or we are looking at
yellow versus green the yellow allele.
Let us ask the question what is the probability
of getting the homozygous recessive in both
cases. Now if you recall a dihybrid cross,
you probably have in the back of your mind
that it was at that very bottom corner and
there were 16 squares of 1/16 probability.
But let us prove it with mathematics. If we
split the two alleles and show just the round
wrinkled locus in one monohybrid and just
the green in the other monohybrid and we combine
those probabilities, what is it? Is it AND
or OR? We are looking for wrinkled AND green.
So we multiply those probabilities. We know because
we already know about monohybrid crosses with
heterozygotes that we would have this possibility
of 1/4. We have got a good visual of that so
we do the mathematics behind it. 1/4 x 1/4
indeed does equal 1/16. Are your trust levels
going up for probability? Because it is a really
cool technique. So here I merely have a question,
we are moving on to a different topic, but