There are 5 coins. Two of them have heads on both sides. One of them have tails on both sides. Two of them are normal coins.

We choose randomly one of those coins and toss it.

1) What is the probability of getting heads?

2) What is the probability of heads on the bottom side of coin provided that we got heads in our toss?

My attempt

1) $$P(H)=\frac{2}{5}+\frac{2}{5}\cdot \frac{1}{2}$$

2) $$P(H_{bot} \mid H)=\frac{\frac{2}{5}}{\frac{2}{5}+\frac{2}{5}\cdot \frac{1}{2}}$$

is that correct?

• Yup, looks good. – Alex G. Jun 13 '15 at 19:47