8: Back to Probability

Let’s say you wanted to figure out how many vampiric but non-fluffy mice would come out of a Ttff crossed with ttFf (the same cross we just did on the last page), without drawing a Punnett Square. How could you do it?

The first step would be to figure out what genotypes would lead to a vampire mouse.

  • Vampire can only happen in one way: tt
  • .
    Now find the genotypes that lead to a non-fluffy mouse.

  • Non-fluffy can happen in two ways: FF or Ff
  • .

So the mouse’s complete genotype would have to be either ttFF or ttFf. Since these genotypes are mutually exclusive, we can use the Law of OR to add up the probabilities.

P(vampiric but non-fluffy mouse)
= P(ttFF OR ttFf) = P(ttFF) + P(ttFf)

There is only one way that ttFF can occur:

For easy reference:
mother’s genotype = Ttff
father’s genotype = ttFf

= P((mother=t AND father=t AND mother=F AND father=F)
= 0.5 x1 x 0 x 0.5
= 0.0 –> meaning this genotype is not possible

The other genotype is a little trickier.

= P((mother=t AND father=t AND mother=F AND father=f) OR
(mother=t AND father=t AND mother=f AND father=F))

= 0.5 x 1x 0 x 0.5 + 0.5 x 1 x 1 x 0.5
= 0 + 0.25
= 0.25

Finally we can go back to our original equation, and see that:

P(vampiric but non-fluffy)
= P(ttFF OR ttFf) = P(ttFF) + P(ttFf)
=0.0 + 0.25
= 0.25

This is the same result that we found using a Punnett Square. The two methods give exactly the same results, so which one you use depends entirely on convenience and personal preference.