# Set-Up

- Suppose you have a machine that produces random coins. (Thus, the probability of taking a coin from the machine, tossing it, and getting a 'heads' is a random variable.
- Suppose f
_{Q}(q)= 2q for 0<q<1 - If Q = q then P(H|Q=q) = q
- Below graph: f
_{Q}(q) vs q

# Question

- Suppose you take a coin from the Random Coin Machine and toss is. What is the probability of flipping a heads?

# Answer

- P(H) $ = \int_{0}^{1}P(H|Q=q) * fQ(q) dq $

$ = \int_{0}^{1}q^2*q dq $

= $ = 2/3 $