A roulette wheel consists of 38 slots, numbered \( 0,00,1,2, \ldots, 36 \). To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0 and 00 are green, the odd numbers are red, and the even numbers are black. Brad is playing roulette and has landed on black three times after three spins. Brad would like one more spin because they are due for a red. What do you think of Brad's logic? Ahoose the correct answer below. A. Brad is incorrect due to the nonexistent Law of Averages. The fact that Brad had three black spins in a row does not matter. The likelihood the next spin will be a red is about 0.47 . \( 12 \% \) of 50 points B. Brad is correct due to the Law of Large Numbers. As the number of spins increases, the likelihood of having at least one red spin increases. C. Brad is correct due to the Law of Averages. The likelihood of having four black spins in a row is about 0.05 . D. Brad is incorrect due to the nonexistent Law of Large Numbers. The fact that Brad had three black spins in a row does not matter. The likelihood the next spin will be a red is about 0.47 .
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Brad is incorrect due to the nonexistent Law of Averages. The roulette spins are independent events, meaning that each spin has the same probability regardless of previous outcomes. Therefore, the chance of landing on red remains about \( 47\% \), and the previous three black outcomes don't influence the next spin. It's a classic example of gambling fallacy! For a real-world application, understanding that past spins do not determine future spins can save players from heavy losses driven by false beliefs. Knowing the probabilities helps players make informed decisions. It’s essential to remember that in games of chance like roulette, every spin is a fresh start!
