Problem

c. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)? A. Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant probability. B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability. Probability Distribution for $x$ C. Since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (b) is the relevant probability. D. Since the probability of getting 1 girl is the result from part (a), this is the relevant probability. \begin{tabular}{c|c} \hline $\begin{array}{c}\text { Number of } \\ \text { Giris } x\end{array}$ & $\boldsymbol{P}(\boldsymbol{x})$ \\ \hline 0 & 0.002 \\ \hline 1 & 0.037 \\ \hline 2 & 0.108 \\ \hline 3 & 0.178 \\ \hline 4 & 0.350 \\ \hline 5 & 0.178 \\ \hline 6 & 0.108 \\ \hline 7 & 0.037 \\ \hline 8 & 0.002 \\ \hline \end{tabular}

Solution

Step 1 :The question is asking which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births. From the table, we can see that the probability of getting 1 girl is 0.037.

Step 2 :The question is asking us to compare this probability with the probabilities of getting 0 girls or more than 1 girl.

Step 3 :The probability of getting 0 girls is 0.002, which is less than the probability of getting 1 girl.

Step 4 :The probability of getting more than 1 girl is the sum of the probabilities of getting 2, 3, 4, 5, 6, 7, and 8 girls. We need to calculate this sum to compare it with the probability of getting 1 girl.

Step 5 :The probability of getting more than 1 girl is approximately 0.961, which is significantly higher than the probability of getting 1 girl.

Step 6 :Therefore, the probability of getting 1 girl is significantly low compared to the probability of getting more than 1 girl.

Step 7 :This means that the result from part (b), which is the probability of getting more than 1 girl, is the relevant probability for determining whether 1 is a significantly low number of girls in 8 births.

Step 8 :Final Answer: \(\boxed{\text{B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.}}\)

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