Finding Odds in Roulette A roulette wheel has 38 slots. One slot ...

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

1:43 minutes

Problem 4.1.42a

Textbook Question

Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number.

a. What is your probability of winning?

Verified step by step guidance

Step 1: Understand the problem. A roulette wheel has 38 slots: 1 slot is 0, 1 slot is 00, and the remaining 36 slots are numbered 1 through 36. You are betting on the outcome being an odd number. To calculate the probability of winning, we need to determine how many odd numbers are present and divide that by the total number of slots.

Step 2: Identify the odd numbers. The numbers 1 through 36 alternate between odd and even. Therefore, half of these numbers are odd. Calculate the total number of odd numbers as \( \frac{36}{2} = 18 \).

Step 3: Determine the total number of possible outcomes. Since the roulette wheel has 38 slots, the total number of possible outcomes is 38.

Step 4: Calculate the probability of winning. The probability of an event is given by the formula \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Substitute the values: \( P(\text{odd number}) = \frac{18}{38} \).

Step 5: Simplify the fraction if needed. If the fraction \( \frac{18}{38} \) can be reduced, simplify it to its lowest terms to express the probability in its simplest form.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of roulette, it is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you want to find the probability of landing on an odd number, you would count the odd numbers on the wheel and divide that by the total slots.

Favorable Outcomes

Favorable outcomes refer to the specific results that align with the event of interest. In the case of betting on an odd number in roulette, the favorable outcomes are the odd-numbered slots on the wheel. Understanding how many favorable outcomes exist is crucial for calculating the probability of winning your bet.

Total Outcomes

Total outcomes represent all possible results that can occur in a given scenario. In roulette, the total outcomes are the 38 slots on the wheel, which include numbers 1 through 36, 0, and 00. Knowing the total number of outcomes is essential for determining the probability of any event, including the likelihood of landing on an odd number.

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Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number.a. What is your probability of winning?