Construct the probability distribution for the random variable X which pertains to the number of female offsprings in a family of three children with 8 probabilities.
Assuming that the probability of having a male or a female offspring is equal (0.5), we can construct the probability distribution for the random variable X as follows:
X = number of female offsprings in a family of three children
Possible values of X: 0, 1, 2, 3
P(X = 0) = P(FFF) = 0.125
P(X = 1) = P(MFF) + P(FMF) + P(FFM) = 0.375
P(X = 2) = P(MMF) + P(MFM) + P(FMM) = 0.375
P(X = 3) = P(MMM) = 0.125
Therefore, the probability distribution for X is:
X | P(X)
--|-----
0 | 0.125
1 | 0.375
2 | 0.375
3 | 0.125
This means that there is a 12.5% chance of having no female offsprings, a 37.5% chance of having one female offspring, a 37.5% chance of having two female offsprings, and a 12.5% chance of having three female offsprings in a family of three children.