Brandun H. answered • 11/20/17

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Your Math Guide from Pre-Algebra to Calculus, SAT/ACT/GMAT Math Prep

weight1 • value1 + weight2 • value2 = Expected value (aka weighted average)

(1/52) • (40 + 4) + (51/52) • 0 = $0.85

This expected value of $0.85 means that on average, you will win $0.85 per draw for playing this game after many draws. So if your birthday is on the 4th, it is not worth playing this game because the $1 cost is higher than the potential $0.85 winnings. In fact, if your birthday is on the 11th or any day prior, it is not worth playing the game for the same reason. If your birthday is on the 12th, you'll break even. If your birthday is on any day past the 12th such as the 13th-31st, then it is worth playing the game because the expected value will be higher than your cost, but you have to play the game a lot of times in order to see the benefit unless you get really lucky!