Louisiana is busy designing new lottery scratch-off games. In the latest game, B

Question

Louisiana is busy designing new lottery scratch-off games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off one spot: A, B, or C. A can reveal "Loser," "Win

$22,"

or "Win

$3535."

B can reveal "Loser" or "Take a Second Chance." C can reveal "Loser" or "Win

$600600."

On the second chance, the player is instructed to scratch off D or E. D can reveal "Loser" or "Win

$22."

E can reveal "Loser" or "Win

$1515."

The probabilities at A are

0.700.70,

0.190.19,

and

0.110.11.

The probabilities at B are

0.750.75

and

0.250.25.

The probabilities at C are

0.9950.995

and

0.0050.005.

The probabilities at D are

0.60.6

and

0.40.4.

Finally, the probabilities at E are

0.930.93

and

0.070.07.

Draw the decision tree that represents this scenario. Use proper symbols and label all branches clearly. Calculate the expected value of this game.

Choose the correct decision tree below.

O A. . O Q Loser Win $2 Win $35 o & no Loser Loser o Loser (0.995) Win $2 (0.00) Win S600 (0.005) -600 Loser (0.75) - 0 Loser (0.6) o Win $2 "Loser (0.93), Chance0:25) Win $15 Loser (0.70) Win $2, DY0.4) O.AL 2 Loser o lavin $155 Second Chance 0.0715 Loser Win $600 600 Win $2 (0.19)

Explanation / Answer

Solution

The best alternative is option (D)

Exected payoff = 4.23(1/3)+(0.23125)(1/3)+3(1/3) = 2.49

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