Question

A genetics experiment involves a population of fruit flies consisting of 3 males named Alex, Bob, and Carlos and 1 female named Dana. Assume that two fruit flies are randomly selected with replacement. a. After listing the possible samples and finding the proportion of females in each sample, use a table to describe the sampling distribution of the proportion of females. Proportion of females Probability 0.5 1 (Type integers or fractions.)

Answer 1

We would be looking at the first question all parts here as:

Q1) We are given here that there are 3 males and 1 female.

As we are drawing with replacement here, therefore the probability of getting a female remains same in both the draws given as:
p = P(female) = n(Females) / n(Total) = 1/(1 + 3) = 1/ 4 = 0.25

Therefore the number of females in the 2 draws here could be modelled as:

$X \sim Bin(n = 2, p = 0.25)$

The probability distribution table now is computed here as:

Proportion of Females	Probability
0	P(X = 0) = (1 - 0.25)2 = 0.5625
0.5	P(X = 1) = 2*0.25*(1 - 0.25) = 0.375
1	P(X = 2) = 0.252 = 0.0625

These are the required probabilities here.