89.1.19-G

Find the expected payback for a game in which you bet $8 on any number from 0 to 99. If your number comes up you get $400

The expected payback is

(Round to the nearest cent as needed.)

Enter your answer in the answer box and then click Check Answer.

$48.00

-$4

Step-by-step explanation:

The expected payback formula is the sum of probability multiply the value

E (x) = p (x1) * x1 + p (x2) * x2 + ...

In this case, we have two possibility of payback

1) winning

The payback is $400 - $8 = $392

x1 = 392

The probability of winning is one out of 100 (since the choices are 0 to 99)

p (x1) = 1/100

2. Losing

The payback is - $8 since the person didn't win anything is loose

x2 = - 8

Since there is only one winning number, the other 99 numbers are loosing numbers

p (x2) = 99/100

Therefore expected payback is

E (x) = p (x1) * x1 + p (x2) * x2

= (1/100) * 392 + (99/100) * (-8)

= - 400/100

= - $4