When two births are randomly selected, the sample space for genders is bb, bg, g

Question

When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is, the probability of having a girl is ), and this is not affected by how many boys or girls have previously been born. Determine the probabilities of each sample proportion. Sample proportion of girls Probability (Type integers or simplified fractions)

Explanation / Answer

here there are 4 outcomes where each outcome has equal probability

hence for oucome bb; sample proportion for girls =0/2 =0(as there are 0girls among two chidren) and its probability =1/4 cause it is one outcopme of 4 outconmes of sample space

hence below is the table

sample proportion of girls probability 0    1/4 1/2 1/2 1    1/4

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