Question

You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $1; if the faces are both heads, you win $2; if the coins do not match (one shows a head, the other a tail), you lose $1 (win (−$1)). Give the probability distribution for your winnings Y on a single play of this game.

Answer 1

Explanation:

Given that you and a friend play a game where you each toss a balanced coin.

If the upper faces on the coins are both tails, you win $1;

if the faces are both heads, you win $2;

if the coins do not match (one shows a head, the other a tail), you lose $1 (win (−$1)).

Let Y be the amount won

Then Y can take values as 1,2 and -1

`P(Y=1) =P(TT) = 0.25\\P(Y=2) = P(HH) = 0.25\\P(Y=-1) = P(HT)+P(TH) = 0.5`

The above is the probability distribution for Y.