Step 1 :In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 36 times, we are asked to find the probability of the ball falling into the green slots 5 or more times.
Step 2 :The probability of the ball falling into a green slot in a single roll is \(\frac{2}{38}\), since there are 2 green slots out of a total of 38 slots.
Step 3 :This is a binomial probability problem, where the number of trials is 36, the number of successful trials is 5 or more, and the probability of success on a single trial is \(\frac{2}{38}\).
Step 4 :The binomial probability formula is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(P(X=k)\) is the probability of \(k\) successes in \(n\) trials, \(C(n, k)\) is the number of combinations of \(n\) items taken \(k\) at a time, \(p\) is the probability of success on a single trial, \(n\) is the number of trials, and \(k\) is the number of successful trials.
Step 5 :However, since we want the probability of 5 or more successes, we need to sum up the probabilities for 5, 6, 7, ..., 36 successes.
Step 6 :Using the binomial probability formula and summing up the probabilities for 5 to 36 successes, we get a probability of approximately 0.039.
Step 7 :Final Answer: The probability that the ball falls into the green slots 5 or more times is approximately \(\boxed{0.039}\).