Place the solution steps in the correct order: In American roulette, the wheel contains the numbers 1 through 36 , alternating between black and red. There are two green spaces numbered 0 and 00 . A player places a bet of \( \$ 1.75 \) on red to play the game. If the ball lands on red, the player get a \( \$ 1.75 \) for winning and receives the money back. If the ball does not land on red, then the player simply loses the \( \$ 1.75 \) placed on the bet. If the player places the same bet on red 7 .times, what is the player's expected winnings?

To calculate the player's expected winnings, first, consider the probability of landing on red. In American roulette, there are 18 red numbers, 18 black numbers, and 2 green numbers (0 and 00), totaling 38 numbers. The probability of winning on red for a single bet is 18/38. Then, multiply the probability of winning by the payout, which is \( \$ 1.75 \) (the winnings). For the probability of losing, calculate it as 20/38 (including black and green). Finally, consider the player’s total bets over 7 rounds and calculate the expected winnings vs. losses accordingly. This analytical approach ensures a thorough understanding of the game's mechanics and helps make informed betting decisions! For real-world application, understanding the probabilities in roulette can enhance your decision-making skills in gambling or any scenario involving risk and reward. By breaking down each outcome, you can better evaluate potential winnings and losses. It’s crucial to remember that while the game has elements of chance, analyzing the odds can lead to more mindful betting and improved strategies whether you're playing casually with friends or in a casino!