To determine the probability of picking a green disk, we start by analyzing the information given in the question. The table provides the probabilities for picking disks of three specific colors: Red, Blue, and Brown. The probabilities are as follows:
- Probability of picking a red disk (P(Red)) = 0.1
- Probability of picking a blue disk (P(Blue)) = 0.25
- Probability of picking a brown disk (P(Brown)) = 0.3
We know that the total probability for picking any disk from the bag must be equal to 1, because probability is a measure of certainty for all possible outcomes, and we are certain that a disk selected will have one of the given colors.
The total probability (P(Total)) is given by the sum of the probabilities of all the colors:
[tex]\[ P(Total) = 1.0 \][/tex]
Given that there are no other colors besides Red, Blue, Green, and Brown, we can write:
[tex]\[ P(Total) = P(Red) + P(Blue) + P(Green) + P(Brown) \][/tex]
To find the probability of picking a green disk (P(Green)), we rearrange the equation to solve for [tex]\( P(Green) \)[/tex]:
[tex]\[ P(Green) = P(Total) - (P(Red) + P(Blue) + P(Brown)) \][/tex]
Now, we substitute the values we have for the given probabilities:
[tex]\[ P(Green) = 1.0 - (0.1 + 0.25 + 0.3) \][/tex]
Next, we perform the addition inside the parentheses:
[tex]\[ 0.1 + 0.25 + 0.3 = 0.65 \][/tex]
Therefore, we have:
[tex]\[ P(Green) = 1.0 - 0.65 \][/tex]
Finally, we subtract to find the probability of picking a green disk:
[tex]\[ P(Green) = 0.35 \][/tex]
So, the probability of picking a green disk is:
[tex]\[ P(Green) = 0.3500000000000001 \][/tex]
This small discrepancy beyond [tex]\(0.35\)[/tex] occurs due to floating-point precision in calculations, but for practical purposes, we usually refer to it as approximately [tex]\(0.35\)[/tex].
Thus, the probability of picking a green disk is [tex]\(0.35\)[/tex].
