Final answer:
Solving for the probability using the given information, we find that it is approximately 0.008310%.
Step-by-step explanation:
To find the probability of forming a focus group with three females, three males, and three other or non-binary persons, we can use the hypergeometric distribution. This distribution is used when we are sampling without replacement from a population composed of two groups. In this case, the two groups are females and males + others.
We have 582 females, 408 males, and others + non-binary. The total population size is 582 + 408 + 30 = 1020.
Now, we can calculate the probability using the formula:
P(X = k) = (C(n1, k) * C(n2, r - k)) / C(N, r)
Where:
n1 = number of females = 582
n2 = number of males + others = 408 + 30 = 438
r = sample size = 3 females + 3 males + 3 others = 9
N = total population size = 1020
We want to find the probability of X = 3 females, 3 males, and 3 others, so k = 3.
Substituting the values into the formula:
P(X = 3) = (C(582, 3) * C(438, 9 - 3)) / C(1020, 9)
Calculating the combinations:
P(X = 3) = (238625076 * 286 - 151027500) / 69633550996
Simplifying the expression:
P(X = 3) = 5785402 / 69633550996
So, the probability of forming a focus group with three females, three males, and three other or non-binary persons is approximately 8.310 * 10^-5, or 0.008310%.