Question

Find the expected value of the winnings

from a game that has the following payout
probability distribution:
Payout ($) 0 1 3 9 27
Probability 0.67 0.22 0.07 0.03 0.01
Expected Value = [?]
Round to the nearest hundredth.
Enter

Answer 1

To find the expected value of the winnings, we need to multiply each possible payout by its corresponding probability and then add up the results. Mathematically, this can be expressed as:

Expected Value = (0)(0.67) + (1)(0.22) + (3)(0.07) + (9)(0.03) + (27)(0.01)

Expected Value = 0 + 0.22 + 0.21 + 0.27 + 0.27

Expected Value = 0.97

Therefore, the expected value of the winnings is $0.97. Rounded to the nearest hundredth, this is $0.97.