Question

Suppose you stand at a roulette table for five spins of the

wheel. What is the probability of the ball landing on a red number
at most 3 times?

Answer 1

The probability of the ball landing on a red number at most 3 times in 5 spins of the roulette wheel is approximately 1.052.

Step-by-step explanation:

To calculate the probability of the ball landing on a red number at most 3 times in 5 spins of the roulette wheel, we need to consider all possible outcomes.

1. The total number of outcomes for each spin is 37 (18 red numbers, 18 black numbers, and 1 green number).
2. We need to find the probability of getting 0, 1, 2, or 3 red numbers in the 5 spins.
3. Using the binomial probability formula, the probability of getting exactly k red numbers in n spins is given by:
   1. P(k red numbers in n spins) = (nCk) * (p^k) * (q^(n-k)), where p is the probability of getting a red number (18/37), q is the probability of not getting a red number (19/37), n is the number of spins (5), and k is the number of red numbers.
   2. For each k, we calculate the probability and sum them up:

• P(0 red numbers in 5 spins) = (5C0) * ((18/37)^0) * ((19/37)^5) = 0.2357
• P(1 red number in 5 spins) = (5C1) * ((18/37)^1) * ((19/37)^4) = 0.4091
• P(2 red numbers in 5 spins) = (5C2) * ((18/37)^2) * ((19/37)^3) = 0.3051
• P(3 red numbers in 5 spins) = (5C3) * ((18/37)^3) * ((19/37)^2) = 0.1021

The probability of getting at most 3 red numbers in 5 spins is the sum of the probabilities calculated above:

• P(at most 3 red numbers in 5 spins) = P(0 red numbers) + P(1 red number) + P(2 red numbers) + P(3 red numbers) = 0.2357 + 0.4091 + 0.3051 + 0.1021 = 1.052