On a practice exam from statistics I encountered a very difficult exercise I couldn't manage to solve:
In the tent next to you there is a family with two children. Early in the morning you see a boy coming out of the tent. What is the probability that the other child is a girl?
Use Bayes' Rule
My approach to the solution was the following:
We assume $P(GIRL)$ = 0.5 and similarly $P(BOY)$ = 0.5.
We have to compute the following conditional probability: $P($One child is a girl| One child is a boy).
By applying Bayes' rule we should be able to compute this probability.
Bayes Rule: $P(A|B)$ $=$ $\frac{P(B|A)*P(A)}{P(B|A)*P(A) + P(B|A^c)*P(A^c)}$
Could anyone please help me with this, I tried many things but nothing worked out..