## Friday, August 04, 2017

### Ruminate on this!

No doubt you enjoy puzzles:

There is a group of animals, one third of which are sheep. One animal was examined and found to have four legs. The scientist who did that examination tells us that the result “four legs” was three times more likely if the examined animal was a sheep than if it was not a sheep. What is the probability that the examined animal was a sheep?

Most trial lawyers should be able to correctly answer that almost instantly. The answer is in the comment posted by me.

#### 1 comment:

Don Mathias said...

Time's up! Pens down!

The problem gives the priors and the likelihood ratio.

The priors are: Probability of it being a sheep = 0.33, over the probability of it being a "not sheep" = 0.67 = 1 to 2.

The likelihood ratio as given is 3 to 1.

So the probability of it being a sheep, over the probability of it being a "not sheep" is 1/2 times 3/1 = 3/2.

So the probability of it being a sheep is 3 out of 5 or 0.6.

Answer: 0.6.