Independent Events

Joint Probability

The joint probability of two independent events is the product of the individual probabilities of each event.

P(A)gamete = P(a)gamete = 1/2
P(B)gamete = P(b)gamete = 1/2
P(AB) = P(Ab) = P(aB) = P(ab) = 1/2 x 1/2 = 1/4
* Provided that the genes are not linked.

Testcrosses

Testcross - cross an F₁ heterozygote to a double homozygous recessive.
AABB x aabb AaBb(F₁)

AaBb x aabb is the F1 testcross.

Results in a 1:1:1:1 (Ho:1:1:1:1 Type 1 error - reject
Ho when it is true) ratio and completely reveals genotype of F₁, regardless of dominance gene action at each locus. The relative frequencies of the gametes of the heterozygous parent can be observed in the testcross progeny.

Examples

Probability of an event is the proportion of times that an event is expected to occur in numerous repeated trials. Relative frequency is the actual number of events divided by the total number of events.

Example 1:

Probability of a head in a coin toss = 1/2. If we
toss a coin 50 times and count 20 heads and 30
tails, the relative frequency of heads is 20/50 =
0.4. The probability of a head is 25/50, assuming
the coin is balanced. If we continued to toss the
coin, the relative frequency of heads would
approach 1/2 as the number of coin tosses
approached infinity. Probability is an abstract
concept of what we would expect in the long run.

If two events are independent, we can multiply
the probabilities of each event to determine the
probability of both events occurring.

If the probability of one event is not influenced
by the probability of a second event, the events
are independent.

Example 2:

Prob. (boy) = 1/2
Prob. (girl) = 1/2

Probability of a boy being born as the first child
and a girl born as the second child is
1/2 x 1/2 = 1/4.