Suppose you have a weighted coin in which heads comes up with probability 3/4 and tails 1/4 with probability . If you flip heads, you win 2 but if you flip tails, you lose 1 What is the expected win of a coin flip in dollars?

 Jun 5, 2021

The expected amount of money you will win from this is 


$\frac{3}{4} \cdot 2 + \frac{1}{4} \cdot -1 = \boxed{\frac{5}{4}}$, which is the expected win amount of the coin flip. 


This is essentially multiplying the probability of each scenario (heads and tails), with the amount of money you would win theoretically if you flipped that scenario. 


Even if you will never win exactly $\frac{5}{4}$ dollars in a coinflip, it's essentially an average of how much you would profit on average for each coin flip. 

 Jun 5, 2021

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