Slide 1
Punnett squares are useful tools for making predictions about
simple genetic crosses. However, they quickly become cumbersome when we
advance our genetic analysis to multiple genes.
For more advanced genetic analysis, probability theory is an easier way to make predictions about future offspring.
Slide 2
There are two rules of probability you need to be aware of - the
rule of multiplication and the rule of addition.
We will look at the rule of multiplication first.
The Rule of Multiplication says that to determine the probability of an event occurring, determine the individual probabilities of each independent event, and then multiply the individual probabilities to obtain the probability of these events occurring together.
Another way to think about this is that if you use the word "and" you multiply. Let's look at an example to demonstrate this.
What is the probability of rolling a 5 and then a 3 with a fair die?
Notice this question uses the word "and" - so you need to determine the probability of rolling a 5 (1/6) and the probability of rolling a 3 (1/6) and multiply these individual probabilities together.
Slide 3
So, the overall probability of rolling first a 5 and then a 3 is
1/36.
Slide 4
The second rule you need to know is the rule of addition.
The Rule of Addition says that if an event can occur in more than one way, the
probability of that event occurring is equal to the sum of the probabilities
of each different way that the event can occur.
Another way to think about this rule is that you are using the word "or" so you need to add. Let's look at an example to demonstrate this.
What is the probability of rolling a 5 when rolling 2 dice?
First, you
need to recognize that there are four different ways to roll a 5 - you can
roll a 3 and a 2, OR a 2 and a 3, OR a 4 and a 1, OR a 1 and a 4. Each
die is unique and you need to consider each die independently.
The probability of rolling a 3 and 2 is 1/6 x 1/6= 1/36.
The probability
of rolling a 2 and 3 is 1/6 x 1/6= 1/36.
The probability of rolling a 1 and
4 is 1/6 x 1/6= 1/36.
The probability of rolling a 4 and 1 is 1/6 x 1/6=
1/36.
To determine the overall probability of rolling any one of these combinations you add the individual probabilities together.
Slide 5
So the overall probability is 4/36.
Slide 6
So let's apply these rules to a three gene genetics problem.
Assume you have an F1 generation that is heterozygous for 3 genes - genes A,
B, and C. What is the probability of them having an offspring with
genotype aabbcc? What is the probability of them having an offspring
that is heterozygous for all three genes?
Remember, if you use a Punnett square, you will need an 8 x 8 or 64 square Punnett square! Using probability will be much easier once you get the hang of it. Once you have the answers - access the next VoiceThread.