Question3. Genetics Suppose a married man and woman both carry a gene for cystic fibrosis but don't have the disease themselves. According to the laws of genetics, the probability that their first child will develop cystic fibrosis is 0.25 . (a) Explain what this probability means. (b) If the couple has 4 children, is one of them guaranteed to get cystic fibrosis? Explain.
Studdy Solution
STEP 1
What is this asking? If two parents carry a cystic fibrosis gene, what's the chance their first child has the disease, and does having four kids guarantee one will have it? Watch out! Don't mix up the probability for *one* child having the disease with the probability for *multiple* children.
STEP 2
1. Explain Probability
2. Four Children Case
STEP 3
Alright future geneticists!
We're told there's a probability of the first child having cystic fibrosis.
STEP 4
What does this *really* mean?
It means that if we looked at *many, many* similar couples having *one* child, about of those children would develop cystic fibrosis.
It's *not* a guarantee for any *single* couple.
STEP 5
Now, what about four children?
Does that guarantee at least one child with cystic fibrosis?
Not quite!
STEP 6
Let's think about it this way: there's a chance the *first* child has the disease.
That means there's a chance the first child *doesn't* have it.
STEP 7
Since each child inherits the gene independently, the probability of *none* of the four children having cystic fibrosis is multiplied by itself four times:
STEP 8
So, there's roughly a chance that *none* of the four children will have the disease.
That means it's *not* a guarantee that at least one will have it.
STEP 9
(a) The probability means that out of many similar couples having one child, about of those children would have cystic fibrosis.
It's not a guarantee for any individual couple.
(b) No, having four children doesn't guarantee one will have cystic fibrosis.
There's about a chance that *none* of the four children will have the disease.
Was this helpful?
