Question

Henry flips 10 coins and lays them on the desk. He then chooses one of the coins at random, and if it is tails, he flips it to heads. What is the expected number of heads showing?

a) 4
b) 5
c) 6
d) 7

Answer 1

The expected number of heads showing after flipping 10 coins and then flipping one that was tails is 5, as initially expected 5 heads plus an additional 0.5 heads from the extra flip rounds down to 5.

Step-by-step explanation:

The question asks us to determine the expected number of heads showing after flipping 10 coins and then flipping one additional coin that was initially tails. With 10 coins, the expected number of heads is initially 5, as there is a 50 percent chance of getting heads on any given flip (assuming the coins are fair). If Henry chooses one coin at random, there is a 50 percent chance it is tails. If it is tails, he flips it to heads. This adds an expected 0.5 heads to our initial 5, giving an expected total of 5.5 heads. Since we cannot have half a head, we consider the whole number that is closest to the expected value, without exceeding it, which is 5. Therefore, the expected number of heads showing is 5.