Final answer:
To calculate the probability of selecting at least one red ball, use the complement rule: one minus the probability of selecting no red balls, which can be computed with combinations.
Step-by-step explanation:
The student is asking for the probability that at least one red ball is chosen when six balls are randomly selected from an urn containing 8 red, 10 green, and 12 blue balls. To solve this, we can use the complement rule. The total number of balls in the urn is 8 red + 10 green + 12 blue = 30 balls. The complement rule states that the probability of 'at least one red ball' is equal to one minus the probability of 'no red balls'. To find the probability of choosing six balls with none being red, we would calculate the probability of choosing six balls from the 22 non-red balls (green and blue). This would be a combination of 22 balls taken 6 at a time, which can be computed using the combination formula C(n, k) = n! / (k!(n-k)!), and compare this to the total possible combinations of choosing any six balls from the 30 total balls.
The probability of no red balls is C(22, 6) / C(30, 6). Thus, the probability of selecting at least one red ball would be 1 - (C(22, 6) / C(30, 6)). When you compute these values, you get the exact probability of drawing at least one red ball in your selection.