# Thread: Probability problem

1. ## Probability problem

A doctor says that a infant who predominantly turns the head to the
right will be right-handded and the one who turns the head to the left
will be left-handed. The newborn baby girl turned her head to the left.
Given that 90% of the population is right-handed, what is the probability
of baby being right handed if the test is 90% accurate ? What if it is
80% accurate ?

I got 0.5 for the first question and 0.6923 for the second, is this correct?

2. I think you need to use the Bayes formula.

[P(A)P(ClA)]/[(P(A)P(ClA))(P(B)P(ClB))...]

P(A) = .9
P(B) = .1
P(ClA) = .9
P(ClB) = .1

[(.9)(.9)]/[(.9)(.9)+(.1)(.1)]
.81/.82
98.78%

P(A) = .9
P(B) = .1
P(ClA) = .8
P(ClB) = .2

[(.9)(.8)]/[(.9)(.8)+(.1)(.2)]
.72/.74
97.3%

Oops, I don't think this is right.

3. Originally Posted by bsqrs
A doctor says that a infant who predominantly turns the head to the
right will be right-handded and the one who turns the head to the left
will be left-handed. The newborn baby girl turned her head to the left.
Given that 90% of the population is right-handed, what is the probability
of baby being right handed if the test is 90% accurate ? What if it is
80% accurate ?

I got 0.5 for the first question and 0.6923 for the second, is this correct?
I get the same, to four decimal places (actually I get the exact answers of 1/2 and 9/13).