Question

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:

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.

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