Naveen's coin box contains 8 fair standard coins (heads and tails) and 1 coin which has heads on both sides. He selects a coin randomly and flips it 4 times, getting all heads. If he flips this coin again, what is the probability it will be heads?
Coin tosses are independent.
P(Head) = P(Head/Fair Coin)P(Fair Coin) + P(Head/Unfair Coin)P(Unfair Coin)
= 1/2 * 8/9 + 1 * 1/9
= 4/9 + 1/9
Am I right?