Consider a lottery with four possible outcomes, $A , B , C$, and D. The associated payoffs are: $\$ 10$, $\$ 30 , \$ 70$, and $\$ 150$, respectively. The probabilities are $P ( A ) = 0.40 , P ( B ) = 0.20 , P ( C ) =$ $0.30$, and $P ( D ) = 0.10$. The expected value of this lottery is what?

Question

Quizplus · Accepted Answer

The expected value of the lottery is calculated as follows:
$$E(X) = 0.40(\$ 10) + 0.20(\$ 30 + \$ 70) + 0.30(\$ 70) + 0.10(\$ 150) = \$ 46$$
Therefore, the expected value of the lottery is $\$ 46$. The best choice is to play the lottery since the expected value is positive. However, note that this does not guarantee a win, but over many trials, the average payoff would be close to $\$ 46$ per play. To find the expected value, we multiply each payoff by its associated probability, and then add up the products. So, the expected value is:
$$(0.40)(\$10) + (0.20)(\$30 +\$ 70) + (0.30)(\$150) + (0.10)(\$0) = \$4 + \$20 + \$70 + \$0 = \$94$$
Therefore, the expected value of the lottery is $\$94$. The best choice is option B because it has the highest expected value.

Consider a Lottery with Four Possible Outcomes A,B,CA , B , CA,B,C

Consider a Lottery with Four Possible Outcomes $A , B , C$