I’m commenting on the expected value.
There is a 1/2 probability to win $50 million. So $50 million Pr{win} = 50 million x 1/2 = $25 million.
However, you are not placing a bet in this case (you are not putting in any money to win $50 million). So I don’t see how expected value can be useful.
Imagine that you pay $4 million to be able to press the green button.
The expected value would be:
0.5 x $50 million + 0.5 x (-$4 million) = $23 million.
This would mean that in the long run (if you bet more than once) your bet would win. Because you would be “expected” to “win” $23 million every time you hit the button.
You would only have negative expected value if you bet more than $50 million, which would be silly.
In case you hit the green button or not, you are not betting anything. Also, you could only press once. Expected value is good when you are going to place more than one bet.
