Lottery game: Suppose you select two green numbers (from 1 to 26) and two black

Question

Lottery game:

Suppose you select two green numbers (from 1 to 26) and two black numbers (from 1 to 26) The cost to play is $1 if you select all four correctly you will win grand prize of 22,000

Find the expected value (winning the grand prize) of one play of this lottery

You can still win $3 if you correctly choose two balls and their color correctly. Either the two green correct and two black incorrect or two black correct and two green incorrect. Find the probability and decide whether the payoff looks suitable.

Explanation / Answer

Total no. of combinations = 26C2 * 26C2 = 26*25/2 * 26*25/2 = 325*325 = 105625

Probabiltiy of winning = 1/105625

Probability of losing = 105624/105625

E(x) = 1/105625* (21999) - 1*105624/105625 = -0.79

Probability of winning = 2/26C2 * 24C2/26C2 = [2/325]*[24*23/(26*25)] = 0.00522

E(x) = 1/105625* (21999) + 2* 0.00522 -1 *[1-1/105625 -.00522] = -0.776

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