In new Jersey Pick 4 lottery game, you pay 50 cents to select a sequence of four

Question

In new Jersey Pick 4 lottery game, you pay 50 cents to select a sequence of four digits, such as 1332. If you select the same sequence of four digits that are drawn, you win and collect $2788? a] How many different selections are possible?

b] What is the probability of winning?

c] If you win, what is your net profit?

d] Find the expected value?

e] If you bet 50cents in Illiois Pick 4 game, the expected value is -25 cents. Whihc is a better bet A 50 cents bet in the illionois pick 4 game or a 50cents bet in New Jersey Pick 4 game? Explain.

for letter a why is it 1/10000

Explanation / Answer

There are 10 X 10 X 10 X 10 = 104 = 10,000 different possible selections. Accordingly the probability of winning is 1/10,000 = 0.0001. If you win, you will have invested 50¢ and won $2,788, for a net profit of $2,787.50. Your expected value is 0.0001(2,787.50) + 0.9999(–.50) = 0.27875 – 0.49995 = – 0.2212 or –22.12¢ The Pick-4 game is better because losing 22.12¢ isn’t as bad as losing 25¢.

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