Research on learning abilities of mice

[superwolf]

Homework Statement

We want to test the learning abilities of mice. We put them in a maze. If they choose to go to the right, they will find food. If they go to the left, there's nothing.

Assuming that P(right) = P(left) = 0.5 the first try, P(right) = P(left) = 0.5 the second try given that the mouse chooses left the first try, and P(right) = F the second try given that the mouse chooses right the first try - what is the chance that the mouse chose right in the first try, given that it chose right in the second try?

2. Attempt

$$P(A|B) = \frac{P(B \cap A)}{P(A)} = \frac{F / 2}{1/2}= F$$

Correct answer: $$\frac {2F}{2F+1}$$

 

[yyat]

Check your formula for the conditional probability, there should be a P(B) in the denominator.