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You and a friend play a game where you each toss a
Chapter 3, Problem 2E(choose chapter or problem)
Problem 2E
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.
Questions & Answers
QUESTION:
Problem 2E
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:
Solution 2E
Step1 of 3:
Let us consider two fair coins, if upper faces of coins are both tails then you win $1. If upper faces of coins are both heads then you win $2; if the coins do not match then you lose $1.
Let us consider an event ‘H’ be the heads.
Let event ‘T’ be the tail.
Consider the sample space S = {H, T, H, T}
Our goal is:
We need to Give the probability distribution for your winnings, Y , on a single play of this game.
Step2 of 3:
Let us consider two fair coins, if we toss both coins at the same time then the probability of getting both are tail is given by:
P(TT) =
=
Similarly,
P(HH) =