Conditional Probability
If two events are NOT independent, the
Probability(A and B) equals Probability(A) x
Probability(B/A). The Probability(B/A) is conditional probability and
is read as the probability of event B given that event A has already
occurred.
| AaBb
0.4 |
aaBb
0.1 |
0.5
= P(Bb) |
| Aabb
0.1 |
aabb
0.4 |
0.5
= P(bb) |
| 0.5
= P(Aa) |
0.5
= P(aa) |
1.0 |
P(Aa) = 0.5 is a marginal probability.
The conditional probability of an Aa genotype given that the genotype
is Bb is:
| Probability(Aa/Bb) = |
Probability(Aa and Bb) |
| Probability(Bb) |
| Probability(Aa/Bb) = |
Probability(AaBb) |
= |
0.4 |
= 0.8 |
| Probability(Bb) |
0.5 |
The conditional probability that a Bb genotype will also have the Aa
genotype = 0.8.
If we know that a genotype is Bb, then the probability of that genotype
being Bb is unity.
We have reduced the sample space because the sample space no longer
includes the Aabb or aabb genotypes. We have reduced the sample space
to include only the events that consist of the probability of the Bb
genotype. The probability of an AaBb genotype is greater when we already
know that the genotype of the second locus is Bb.
| AaBb
0.8 |
aaBb
0.2 |
1.0
= P(Bb) |
P(AaBb) = Probability(Aa/Bb) x Probability(Bb) = 0.8(0.5)
= 0.4
