Answer:
Sample space = 216 elements
a) P = 25/72
b) P = 91/216
Step-by-step explanation:
If each die has six possible values, the number of possible outcomes for three dice is 6^3 = 216 possible outcomes
a)
If we want exactly one die to be red, we have that one die is red (probability of 1/6) and the other two are not red (probability of 5/6), and the red die can be any of the three dice (combination of 3 choose 1), so the probability is:
P = C(3,1) * (1/6) * (5/6) * (5/6) = 3 * 25/216 = 75/216 = 25/72
b)
To find the probability of at least one die is red, we can find the probability of all dice not being red, and then find the complement of this probability (1 - P).
The probability of one die not being red is 5/6, so we have:
probability of all dice not being red = (5/6)^3 = 125/216
probability of at least one die being red = 1 - 125/216 = 91/216
