A gene can be either type A or type B, and it can be either dominant or recessive. If the gene is type
B, then there is a probability of 0.31 that it is dominant. There is also a probability of 0.22 that a gene is type B and it is dominant. What is the probability that a gene is of type A? .......This question is killing me.

Question

zarkon · Answer

given: $$P(D|B)=.31$$
$$P(B,D)=.22$$

so

$$.31=P(D|B)=\frac{P(B,D)}{P(B)}=\frac{.22}{P(B)}$$

thus 

$$P(B)=\frac{.22}{.31}\approx.709677419355$$

$$P(A)=1-P(B)\approx1-709677419355=.290322580645$$