Question

On the planet LongLiveRock, there is a recessive condition known as WhoAreYou. People with this trait have an uncontrollable perform windmill guitar swings. The two alleles at the trait locus are labeled R (trait) and r (wild type). If the probability of transmitting an r allele is 0.54, then what is the probability that any child born to carrier parents will be unaffected (i.e., will not perform windmill guitar swings)?

Answer 1

The probability that any child born to carrier parents will be unaffected is 0.788

Explanation:

WhoAreYou is a recessive condition, that means that both parents should transmit the trait allele (R). The wild type allele (r) is the dominant one, the one that if present, the child is unaffected. That means, we are looking at the cases when there is an r allele present. It's easier to do the math (because if not, we have to take into account more cases than in this way) for r allele not present (two R alleles), knowing that:

`P_{\mbox{r present or not present}}= P_{\mbox{r present}}+P_{\mbox{r not present}}=1`

To know what
`P_{\mbox{r not present}}` is, we know that the probability of transmiting R is 0.46 (1-0.54), and that both parents should transmit it. As each probability is independent from the other, we multiply probabilities:

`P_{\mbox{r not present}}=0.46^(2)=0.212\\ \\P_{\mbox{r present}}=1-P_{\mbox{r not present}}=1-0.212=0.788`