Final answer:
In this game, each player spins the spinner twice in their turn to earn points. We can determine the expected winner by calculating the probability of getting a match and the probability of getting different letters. The expected number of turns can be found using a geometric series.
Step-by-step explanation:
In this game, each player spins the spinner twice in their turn. If the letters on the two spins match, Player One gets 2 points. If the letters are different, Player Two gets 3 points. The first person to reach 20 points wins. To determine which player is expected to win, we need to calculate the probability of getting a match on two spins and the probability of getting different letters on two spins.
The probability of getting a match on two spins is calculated by multiplying the probability of getting a specific letter on the first spin (1/6) by the probability of getting the same letter on the second spin (1/6). This gives us a probability of 1/36. The probability of getting different letters on two spins is calculated by subtracting the probability of getting a match (1/36) from 1, which gives us 35/36.
To determine the expected number of turns before a player wins, we can set up a geometric series. Let x be the expected number of turns. The probability of Player One winning on the first turn is 1/36, and the probability of Player One winning on any other turn is (35/36)^(2x-1) * (1/36). The expected number of turns can be calculated using the formula: x = 1 * (1/36) + x * (35/36)^(2x-1) * (1/36). By solving this equation, we can find the value of x.