'A Prize Wheel' Fraction Problem

[gurbanoğlu]

I have been having difficulty on this one problem. This is the problem: 'A prize wheel at a county fair is divided into 8 equal sections. Each section on the wheel is marked with a letter, and each letter refers to a different stuffed-animal prize. The letter G stands for giraffe, Z for zebra, and M for monkey. If the wheel stops at the letter C, the winner gets to choose a prize. What is the probability that the first 3 people in line will each spin an M?'

There is a prize wheel, and it looked like the attached GIF file.
The choices are: A [27/512] B [27/343] C [9/512] D [1/512]

The way I am approaching this problem is that there are 8 options on the wheel, and there are 3 M slots that can be landed on. The chances of landing on M for each individual is 3/8. However I am failing to understand why the probability changes when you increase the number of consecutive spins. If anything it seems that consecutive spins increase the probability of landing on M. 3/8 X 3/1 = 9/8 which is an increased probability.

 

[pka]

I have been having difficulty on this one problem. This is the problem: 'A prize wheel at a county fair is divided into 8 equal sections. Each section on the wheel is marked with a letter, and each letter refers to a different stuffed-animal prize. The letter G stands for giraffe, Z for zebra, and M for monkey. If the wheel stops at the letter C, the winner gets to choose a prize. What is the probability that the first 3 people in line will each spin an M?'
There is a prize wheel, and it looked like the attached GIF file.
The choices are: A [27/512] B [27/343] C [9/512] D [1/512]

What is \(\displaystyle {\left( {\dfrac{3}{8}} \right)^3} = ?\)

 

[gurbanoğlu]

The answer then is [A]. Thank you for your help.

It makes sense that the answer is (3/8) X (3/8) X (3/8), rather than (3/8) X 3.

Once again thank you for your assistance!