Problem

Sickle cell anemia is an inherited disease in which red blood cells become distorted and deprived of oxygen. A person with two sickle cell genes will have the disease, but a person with only one sickle cell gene will have a mild, non-fatal anemia called sickle cell trait. Using $S$ to represent a healthy gene, and s the sickle cell gene, the table shows the four possibilities for the children of two Ss parents. Find the probability that these parents give birth to a child who is healthy. That is, the child does not have the disease or trait. \begin{tabular}{|cc|cc|} \hline & & \multicolumn{2}{|c|}{\begin{tabular}{c} Second Parent \\ S \end{tabular}} \\ \hline First & S & SS & Ss \\ Parent & s & sS & ss \\ \hline \end{tabular} $P($ child is healthy $)=\square$ (Simplify your answer.)

Solution

Step 1 :Sickle cell anemia is an inherited disease in which red blood cells become distorted and deprived of oxygen. A person with two sickle cell genes will have the disease, but a person with only one sickle cell gene will have a mild, non-fatal anemia called sickle cell trait. Using $S$ to represent a healthy gene, and s the sickle cell gene, the table shows the four possibilities for the children of two Ss parents.

Step 2 :We are asked to find the probability that these parents give birth to a child who is healthy. That is, the child does not have the disease or trait.

Step 3 :The table of possibilities is as follows: \begin{tabular}{|cc|cc|} \hline & & \multicolumn{2}{|c|}{\begin{tabular}{c} Second Parent \\ S \end{tabular}} \\ \hline First & S & SS & Ss \\ Parent & s & sS & ss \\ \hline \end{tabular}

Step 4 :The number of favorable outcomes (healthy child) is 1 (SS), and the total number of outcomes is 4 (SS, Ss, sS, ss).

Step 5 :We calculate the probability as the ratio of favorable outcomes to total outcomes, which is $\frac{1}{4}$.

Step 6 :Final Answer: The probability that these parents give birth to a child who is healthy is $\boxed{0.25}$.

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