Probability

Independent Events

Let A be one outcome of an event.
Let B be a second outcome of an event.

Probability (A) = probability that event A occurs.
Probability (B) = probability that event B occurs.
Probability (A and B) = probability that both events occur. If A and B are independent events, then the probability of A occurring does not influence the probability that event B occurs.

Probability(A and B) = P(A)P(B) = P(AB) when A and B are independent events

Non-Independent Events

Now assume A and B are not independent events. If two loci are linked and r < 0.5, then the probability of a gamete containing an A allele is not independent of the probability that the gamete contains the B allele.

An Independent Events Example

Locus one has two alleles, A and a.
Locus two has two alleles, B and b.

The two loci are on non-homologous chromosomes and are independent.

The testcross AaBb x aabb 1/4 AaBb
The testcross AaBb x aabb     1/4 aaBb
The testcross AaBb x aabb     1/4 Aabb
The testcross AaBb x aabb     1/4 aabb

Probability(A) = Probability(a) = Probability(B)
= Probability(b) = 1/2

Probability(AB) = 1/2(1/2) = 1/4
Probability(Ab) = 1/2(1/2) = 1/4
Probability(aB) = 1/2(1/2) = 1/4
Probability(ab) = 1/2(1/2) = 1/4