> In a population, the $0.01$ are carriers of a genetic stigma that is partially hereditary. If both of the $2$ parents are carriers of the stigma, each of their children has 0.5 probability to be carrier too. If only $1$ of $2$ parents is a carrier, then each of their children has $0.02$
probability of being a carrier too. If none of the parents is a carrier, then all of their children are not gonna be carriers. We assume hereditary is independent from children to children even if the parents are carriers or not. Also, it is independent if for example the one parent is a carrier while the other is not. (Notice that in reality these circumstances differ)
> (A) What is the probability of $2$
children to be carriers while only $1$
parent is a carrier?
> (B) If we know nothing about the parents, what is the probability of a random couple of parents to have $2$
children that are carriers?
> (C) Taking as a fact that $2$
children are carriers, what is the probability of exactly $1$ of the $2$ parents to be a carrier? And what is the probability that both of them are carriers?
I guess i need to use Baye's theorem, still i don't really know how in this case. My general thought on this:
Let $P(B)$ be the probability of both children being carriers, $P(A)$ the probability of one parent to be carrier.
For (A) : $P(B \mid A) = \dfrac{P(B \cap A)}{P(A)}$
For (C): $P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$ if we want one of them(parents) to be carrier.
Even a hit would be valuable. Thanks in advance.
probability of being a carrier too. If none of the parents is a carrier, then all of their children are not gonna be carriers. We assume hereditary is independent from children to children even if the parents are carriers or not. Also, it is independent if for example the one parent is a carrier while the other is not. (Notice that in reality these circumstances differ)
> (A) What is the probability of $2$
children to be carriers while only $1$
parent is a carrier?
> (B) If we know nothing about the parents, what is the probability of a random couple of parents to have $2$
children that are carriers?
> (C) Taking as a fact that $2$
children are carriers, what is the probability of exactly $1$ of the $2$ parents to be a carrier? And what is the probability that both of them are carriers?
I guess i need to use Baye's theorem, still i don't really know how in this case. My general thought on this:
Let $P(B)$ be the probability of both children being carriers, $P(A)$ the probability of one parent to be carrier.
For (A) : $P(B \mid A) = \dfrac{P(B \cap A)}{P(A)}$
For (C): $P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$ if we want one of them(parents) to be carrier.
Even a hit would be valuable. Thanks in advance.