Questions: Question 4 0 / 2 pts 3 99 Details In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. a) Find the probability of winning if you pick the number 33. Leave your answer as a fraction. b) Find the probability of an odd number coming up on the wheel. Leave your answer as a fraction.

Solution Steps

a) To find the probability of winning if you pick the number 33, we need to determine the total number of possible outcomes and the number of favorable outcomes. The total number of spaces on the roulette wheel is 38 (numbers 0 through 36 and 00). The number of favorable outcomes (picking 33) is 1. The probability is the ratio of favorable outcomes to total outcomes.

b) To find the probability of an odd number coming up on the wheel, we need to count the number of odd numbers on the wheel and divide by the total number of spaces. The odd numbers range from 1 to 35, and there are 18 odd numbers in total.

To find the probability of winning by picking the number 33, we calculate the ratio of favorable outcomes to total outcomes. The total number of spaces on the roulette wheel is \( 38 \), and the number of favorable outcomes for picking 33 is \( 1 \). Thus, the probability is given by:

\[ P(33) = \frac{1}{38} \]

Next, we determine the probability of an odd number coming up on the wheel. There are \( 18 \) odd numbers (1, 3, 5, ..., 35) on the wheel. The total number of spaces remains \( 38 \). Therefore, the probability of an odd number is:

\[ P(\text{odd}) = \frac{18}{38} = \frac{9}{19} \]

Final Answer