Calculate probability that a baby is right handed

Question

A doctor says that a baby who predominantly turns his/her head to the right while lying on his/her back will be right-handed and conversely one who predominantly turns to the left will be left-handed. Baby Allie predominantly turned her head to the left. It is known that 90% of the population is right-handed.

What is the probability of Allie being right-handed if the method is 90% accurate? Use the Boolean r.v. TR to mean that a baby turns his/her head to the right, and the Boolean r.v. RH to mean that a baby is right-handed.

My Answer: P(RH | TR) = 0.9 and P(not RH | not TR) = 0.9 P(RH) = 0.90 P(RH(Allie)) = P(RH | not TR) = 1 - P(not RH | not TR) = 0.1

Is the above correct?

Answer 1

Yes, this is correct. Actually, this task is designed to be a catch. You can safely ignore how much of the population is left-handed, because you are given how accurate the method is.

No matter the right/left handed ratio in the population, the "accuracy" of this method is evenly spread across the population.

Answer 2

I think the population statistic is giving you the prior on RH, and the accuracy of the method is the likelihood p(TR | RH). This interpretation allows you to make use of all the information provided---but it's worded a little strangely. I assume this is homework: write both answers, explaining why you have two different results.