Question

Two persons A and B have respectively ($n+1$) and $n$ coins which they toss simultaneously. The probability that A will have more number of heads is

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{8}$

Answer 1

Answer: (C)

$\frac{1}{2}$

Quick Solution:
Well if n is 0, then Player A has 1 coin, and player B has 0 coins. B is guaranteed to have 0 heads. There is a 1/2 chance Player A has 1 head, and a 1/2 chance player A also has 1 head. Therefore the answer should be D) 1/2.
More Detailed Solution:
Well if they had the same number of coins, the most likely outcome is that they would get the same number of heads, and each player has an equal chance of getting more heads than the other player (the chance being less than 1/2). If we give player A one more coin than player B there is a 1/2 chance that player A will gain an advantage (if that extra coin comes out heads). There is a 1/2 chance the coin gives no advantage (it come out tails). Therefore there is a 1/2 chance that player A will obtain more heads than B.