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?

mathisopandcool Jun 5, 2021

#1**+1 **

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.

xCorrosive Jun 5, 2021