1.) The Addition Rule: P(A or B) = P(A) + P(B) - P(A and B)
If A and B cannot occur together, then the third term is 0, and the rule reduces to P(A or B) = P(A) + P(B). For example, you can't flip a coin and have it come up both heads and tails on one toss.
2.) The Multiplication Rule: P(A and B) = P(A) * P(B|A) or P(B) * P(A|B)
If A and B are independent events, we can reduce the formula to P(A and B) = P(A) * P(B). The term independent refers to any event whose outcome is not affected by the outcome of another event. For instance, consider the second of two coin flips, which still has a .50 (50%) probability of landing heads, regardless of what came up on the first flip. What is the probability that, during the two coin flips, you come up with tails on the first flip and heads on the second flip.
Let's perform the calculations: P = P(tails) * P(heads) = (0.5) * (0.5) = 0.25
3.) The Complement Rule: P(not A) = 1 - P(A)
Do you see why the complement rule can also be thought of as the subtraction rule? This rule builds upon the mutually exclusive nature of P(A) and P(not A). These two events can never occur together, but one of them always has to occur. Therefore P(A) + P(not A) = 1. For example, if the weatherman says there is a 0.3 chance of rain tomorrow, let's see the chances of no rain.
P(no rain) = 1 - P(rain) = 1 - 0.3 = 0.7
The rules apply to genetics because they are used to reveal traits that are hidden in the genome by dominant alleles. Probability allows scientists and doctors to calculate the chance that offspring will inherit certain traits, including some genetic diseases.
