1. A bag of colored blocks contains the following assortment of colors:
red (13), blue (12), orange (21), purple (14), green (14), and yellow (6).
Construct the probability distribution for x.
What does x stand for? Red? Blue? Etc.?
To construct the probability distribution for x, we need to first determine the total number of blocks in the bag, which is the sum of the individual color quantities:
Total blocks = 13 + 12 + 21 + 14 + 14 + 6 = 80
Next, we can find the probability of drawing each color by dividing the quantity of each color by the total number of blocks:
Probability of red (P(Red)) = 13 / 80 ≈ 0.1625
Probability of blue (P(Blue)) = 12 / 80 = 0.15
Probability of orange (P(Orange)) = 21 / 80 = 0.2625
Probability of purple (P(Purple)) = 14 / 80 = 0.175
Probability of green (P(Green)) = 14 / 80 = 0.175
Probability of yellow (P(Yellow)) = 6 / 80 = 0.075
Now we can summarize the results in the probability distribution for x:
x | red | blue | orange | purple | green | yellow
---------------------------------------------------------------
P(x) | 0.1625 | 0.15 | 0.2625 | 0.175 | 0.175 | 0.075
This probability distribution shows the probability of selecting each colored block from the bag.