# Conflicting Probability Question (1 Viewer)

#### Jacobagel

##### New Member
This was a question in a biology exam at our school, where the teacher argues that the answer is 50%, whilst the students suggest it is 25%. I thought there was no better place to put the question here, and see what you all think the answer is. The question follows:

"A mum has a 50% chance of having a disease. If she has the disease, her child has a 50% chance of inheriting it from her mum. However, if the mum doesn't not have the disease, the child will not have the disease. What is the probability that the child has the disease?"

#### blyatman

##### Well-Known Member
Basic probability says the answer is 25%.

#### HeroWise

##### Active Member
Id put 25 too lol

#### aa180

##### Member
This was a question in a biology exam at our school, where the teacher argues that the answer is 50%, whilst the students suggest it is 25%. I thought there was no better place to put the question here, and see what you all think the answer is. The question follows:

"A mum has a 50% chance of having a disease. If she has the disease, her child has a 50% chance of inheriting it from her mum. However, if the mum doesn't not have the disease, the child will not have the disease. What is the probability that the child has the disease?"
$\bg_white \text{Let } A \text{ be the event that the child has the disease, and } B \text{ be the event that the mother has the disease. Then, by the given information, we have}$

$\bg_white P(A|B) = 0.5, P(B) = 0.5, P(A|{B}^{c}) = 0. \text{ Now,}$

\bg_white \begin{align*} P(A) &= P(A\cap{B}) + P(A\cap{B}^{c}) \\ &= P(A|B)P(B) + P(A|{B}^{c})P({B}^{c}) \\ &= 0.5(0.5) + 0 \\ &= 0.25. \end{align*}

#### mathsbrain

##### Member
$\bg_white \text{Let } A \text{ be the event that the child has the disease, and } B \text{ be the event that the mother has the disease. Then, by the given information, we have}$

$\bg_white P(A|B) = 0.5, P(B) = 0.5, P(A|{B}^{c}) = 0. \text{ Now,}$

\bg_white \begin{align*} P(A) &= P(A\cap{B}) + P(A\cap{B}^{c}) \\ &= P(A|B)P(B) + P(A|{B}^{c})P({B}^{c}) \\ &= 0.5(0.5) + 0 \\ &= 0.25. \end{align*}
Is the formula you used the law of total probability? Is that in the syllabus?

#### aa180

##### Member
Is the formula you used the law of total probability? Is that in the syllabus?
Yes, you are correct. I don't quite think it is in the syllabus, I just didn't see a way to answer the question without it

#### zoeeoz18

##### New Member
its 25% because 50% x 50% = 25%