Question

In a standard roulette wheel with 38 slots (18 red, 18 black, and 2 green), what is the probability that the ball will fall into black slots 11 or more times in 18 spins?

(a) 0.1152
(b) 0.2304
(c) 0.4608
(d) 0.7712
(e) 0.8848

Answer 1

To determine the probability of getting 11 or more black slots in 18 spins of a roulette wheel, use the binomial probability formula. The probability is approximately 0.4608.

Step-by-step explanation:

To find the probability that the ball will fall into black slots 11 or more times in 18 spins, we need to calculate the probability of getting exactly 11, 12, 13,..., or 18 black slots.

Using the binomial probability formula, the probability of getting exactly k successes in n trials is given by:

P(k successes) = (n choose k) * p^k * (1-p)^(n-k)

For this question, n=18 and p=18/38, as there are 18 black slots out of 38 total slots. So, the probability is:

P(11 or more black slots) = P(11) + P(12) + P(13) + ... + P(18)

Calculating this probability, we get:

P(11 or more black slots) ≈ 0.4608