# Predicting the Outcome of a Cross – Beyond Gregor Mendel

by Georgina Cornwall, PhD

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00:00 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.

00:30 Homozygous recessive, the white flower is a 1/4th probability. Let us look at it mathematically.

00:38 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.

01:43 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.

02:10 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.

02:22 One is by the male parent contributing a little p and the female parent contributing a P.

02:30 The other is by the female parent contributing a p and the male parent contributing a P.

02:38 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 of probability 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.

03:51 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

The lecture Predicting the Outcome of a Cross – Beyond Gregor Mendel by Georgina Cornwall, PhD is from the course Understanding Genetics.

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