In New Jersey\'s Pick 5 lottery game, you pay 75 cents to select a sequence of f

Question

In New Jersey's Pick 5 lottery game, you pay 75 cents to select a sequence of five digits, such as 13321. If you select the same sequence of five digits that are drawn, you win and collect $11, 157. How many different selections are possible? What is the probability of winning? If you win, what is your net profit? Find the expected value. If you bet 50 cents in Illinois' Pick 4 game, the expected value is -25 cents. Which bet is better: A 50 cents bet in the Illinois' Pick 4 game or a 75 cents bet in New Jersey's Pick 5 game? Explain

Explanation / Answer

Solution:

(a) Each of the five positions can be filled with 10 numbers 0,1,2,…,9 to get

10*10*10*10*10 = 10^5 = 100,000

(b) There is only one winning sequence

P (W) = 1/100,000

(c) Net profit is payoff minus the original bet:

$11,157 - $0.75 = $11,156.25

(d)

Expected value = -0.74999 + 0.11157 = -0.63842 or -63.8 cents

5. Since -63.8 cents is less than 25 cents, Illinois has better Pick 4 game.

  

x P (x) x.P (x) -0.75 0.99999 -0.74999 11,157 0.00001 0.11157

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