Let's tackle this problem step-by-step.
a) We have a bowl filled with M&M candies. It includes 20 of each of 6 different colors: brown, yellow, red, blue, green, and orange.
First, we need to determine the total number of candies in the bowl. Since there are 6 colors and 20 candies of each color, the total number of candies can be calculated as follows:
Total number of candies = Number of colors × Number of candies of each color
= 6 × 20
= 120
Next, we need to calculate the probability of choosing any one candy randomly from the bowl. Since each candy has an equal chance of being chosen, the probability is simply the ratio of the number of chosen candies to the total number of candies.
The question specifies that we are choosing one candy at random, so the number of chosen candies is 1.
Therefore, the probability is:
[tex]\[ P(Y) = \frac{\text{Number of chosen candies}}{\text{Total number of candies}} \][/tex]
[tex]\[ P(Y) = \frac{1}{120} \][/tex]
Finally, comparing this with the given options:
[tex]\[ \frac{1}{120}, \frac{10}{120}, \frac{20}{120}, \frac{20}{100}, \frac{1}{20} \][/tex]
We can see that the correct answer is:
[tex]\[ P(Y) = \frac{1}{120} \][/tex]
