Question

game 1 cost 3 dollars has a 0.4 chanve of winning 5 dollars a 0.2 chance of winning 10 dollars and a 0.5 chance of winning nothing. what is the expected value

Answer 1

The possible winnings are $3, $5, $10 and $0.
The corresponding probabilities are 0.4, 0.2 and 0.5.  These add up to 1.1, not 1.0!

Note well:  probabilities must add up to 1.0; ensure that you have copied down the problem correctly.

For illustration purposes only, the expected value here would be the sum of the products of each outcome and its corresponding probability:

$3(0.4) + $10(0.2) + $0(0.5) = $1.20 + $2.00 + $0.00 = $3.20.  This is not the answer, but ony an example of how one would calculate the expected value if the probabilities added up to 1.0 as they must.