Question

A geneticist is studying two genes. each gene can be either dominant or recessive. a sample of 100 individuals is categorized as follows. gene 1 gene 2 dominant recessive dominant 56 24 recessive 14 6 (a) what is the probability that a random sampled individual, gene 1 is dominant (b) what is the probability that a random sampled individual, gene 2 is dominant (c) given that gene 1 is dominant, what is the probability that gene 2 is dominant

Answer 1

Attached is a table. I found the exercise on another page on the internet and the sample of 100 individuals was categorised on a table - easier to understand than as it is presented here.
"(a) what is the probability that a random sampled individual, gene 1 is dominant" - We should first add up all of the individuals that are dominant for gene 1 (56+24) and then divide it by the total number of individuals (100).
$\frac{56+24}{100}$  =0.8
The probability is of 8 in 10 individuals.
"(b) what is the probability that a random sampled individual, gene 2 is dominant" - Follow the same logic as in the previous question.
$\frac{56+14}{100}$ =0.7
The probability is of 7 in 10 individuals.
"(c) given that gene 1 is dominant, what is the probability that gene 2 is dominant" - Because we are considering those that are dominant for gene 1, our total number of individuals is the total individuals that are dominant for gene 1 and not the whole 100. Once we have this restriction, and we want to know the probability that gene 2 is dominant in these individuals, we should also only consider those that are dominant for gene 2.
$\frac{56}{56+24}$ =0.7
The probability that gene 2 is dominant, given that that gene 1 is dominant, is of 7 in 10 individuals.