Question

Suppose that a fair coin is tossed ten times. Each time it lands heads you win a dollar, and each time it lands tails you lose a dollar. Calculate the probability that your total winnings at the end of this game total two dollars, and the probability that your total winnings total negative two dollars.

Answer 1

$2 winning implies we got 2 more heads than tail.

So, in 10 tosses there will be 6 heads and 4 tails

10 105 P(X = $2) = 1024 = 510 0.2051

So, the probability to end with $2 is 105/512 or 0.2051.

b) -$2 winning implies we got 2 less heads than tail.

So, in 10 tosses there will be 4 heads and 6 tails.

P(X = -52) = (40) – (5)** & * - 20, 2011

So, the probability to end with -$2 is 105/512 or 0.2051.

Please comment if any doubt. Thank you.