# 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 fQ(q)= 2q for 0<q<1
• If Q = q then P(H|Q=q) = q
• Below graph: fQ(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?

• P(H) $= \int_{0}^{1}P(H|Q=q) * fQ(q) dq$
$= \int_{0}^{1}q^2*q dq$
= $= 2/3$