Gamblers are playing a game of chance in which they have a 1/40 chance of winning $90. What is the expected payout of this game?
x 0 90
p(x)
x.p(x)
P(x)=1/40
xP(x)=90/40
To find the expected payout of the game, we need to calculate the expected value by multiplying each possible payout by its corresponding probability and summing them up.
In this game, there are two possible outcomes: winning $90 or winning nothing ($0).
The probability of winning $90 is given as 1/40. So, the probability of winning nothing will be 1 - 1/40, which is equal to 39/40.
Now, let's calculate the expected payout:
Expected Payout = (Probability of winning $90) * (Payout of $90) + (Probability of winning $0) * (Payout of $0)
Expected Payout = (1/40) * ($90) + (39/40) * ($0)
Simplifying the equation:
Expected Payout = $90/40 + $0
Expected Payout = $2.25 + $0
Expected Payout = $2.25
Therefore, the expected payout of this game is $2.25.