in roulette, there are 18 red 18 black and 2 green slots

ball rolled 25 times

what is the prob that the ball does not fall into any green slots?

how do you set this up?
I did 1-.0536 and its wrong how to start? thanks so much!

prob of green = 2/38 = 1/19

prob not green = 18/19

now you want this to happen 25 times in a row

prob of your event = (18/19^25 = .2588

To calculate the probability of the ball not falling into any green slots, you need to consider the total number of slots and the number of green slots.

In roulette, there are 18 red slots, 18 black slots, and 2 green slots. Therefore, the total number of slots is 18 + 18 + 2 = 38.

Since the ball is rolled 25 times, each roll is independent of the others. To calculate the probability of an event not happening, you subtract the probability of the event happening from 1.

So, to find the probability of the ball not falling into any green slots, you need to calculate the probability of it falling into a green slot and subtract it from 1.

The probability of the ball falling into a green slot on any given roll is given by the ratio of the number of green slots to the total number of slots. Therefore, the probability of falling into a green slot is 2/38 = 0.0526.

Now, to calculate the probability of not falling into any green slots in 25 rolls, you have to calculate the probability of falling into any slot other than green in a single roll, which is 1 - 0.0526 = 0.9474.

Since the 25 rolls are independent events, you need to multiply the probability of not falling into any green slots in a single roll by itself 25 times:

0.9474^25

Evaluating this expression yields approximately 0.39202.

Therefore, the probability that the ball does not fall into any green slots in 25 rolls is approximately 0.39202, or 39.202%.