A coin is weighted so it comes up heads 34 of the time and t

A coin is weighted so it comes up heads 3/4 of the time and tails 1/4 of the time. You play a game where this coin is flipped. If it comes up heads, you must pay $1. If it comes up tails, you win $2. What is the Expected Value of your winnings in this game? Round and answer in accordance with the previous question. Hint: Pay attention to signs!

Solution

Given that  it comes up heads 3/4 of the time and tails 1/4 of the time.

That means, coin is flipped 4 times. It comes up 3 times head and 1 time tail.

Further given that  If it comes up heads, you must pay $1. If it comes up tails, you win $2.

Hence,

Expected Value of winnings in this game = 3 (head)+ 1 (tail)

= 3 ( - $1) + ($2)

= - 1$

Therefore,

Expected Value of your winnings in this game = - 1$

That means, you will loose 1$ from your pocket at the end of the game.