Cystic fibrosis is a recessive genetic disorder that affects the lungs and digestive system. Amy and Jake are both 

carriers of the recessive allele but do not have cystic fibrosis. What is the probability that they have two children 

who have cystic fibrosis? 

Cystic fibrosis (CF) is caused by a recessive allele, meaning an individual must inherit two copies of the recessive allele (one from each parent) to have the disorder. Since Amy and Jake are both carriers, their genotypes must be heterozygous (CF carrier) for the disease, denoted as **C** (normal allele) and **c** (recessive allele).

### Step 1: Probability for One Child
Using a Punnett square, we can determine the possible outcomes for their offspring:

\[
\begin{array}{c|c c}
 & C & c \\
\hline
C & CC & Cc \\
c & Cc & cc \\
\end{array}
\]

From the Punnett square:
- **CC**: Normal (25%)
- **Cc**: Carrier but unaffected (50%)
- **cc**: Affected with cystic fibrosis (25%)

Thus, the probability of **one child having cystic fibrosis (cc)** is **25%** or **1/4**.

### Step 2: Probability for Two Children
To calculate the probability that two children both have cystic fibrosis, we multiply the probabilities for each child:

\[
P(\text{two children have CF}) = P(\text{first child has CF}) \times P(\text{second child has CF}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}
\]

Thus, the probability that **both children** will have cystic fibrosis is **1/16**.

Would you like further details or any clarifications?

Here are 5 related questions to deepen your understanding:
1. What is the probability that none of their children will have cystic fibrosis?
2. What is the probability that only one child will be affected by cystic fibrosis?
3. If a third child is born, what is the probability that all three children will have cystic fibrosis?
4. Can carriers of cystic fibrosis show symptoms of the disorder?
5. How does the inheritance pattern of other genetic disorders compare to that of cystic fibrosis?

**Tip:** In recessive genetic disorders, carriers do not usually show symptoms because they possess one normal allele, which masks the effects of the recessive allele.

Cystic fibrosis is a recessive genetic disorder that affects the lungs and digestive system. Amy and Jake are both carriers of the recessive allele but do not have cystic fibrosis. What is the probability that they have two children who have cystic fibrosis?

Calculate the probability of Amy and Jake, both carriers of the cystic fibrosis gene, having two children with cystic fibrosis. This problem involves basic probability concepts, the Punnett square method, and genetic inheritance patterns. Suitable for students in Grades 9-12.

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