Final answer:
To find the probability of having 4 girls and 3 boys among the ticket holders, we can use the hypergeometric distribution. By substituting the values into the formula, the probability is calculated to be 0.152 or 15.2%.
Step-by-step explanation:
To find the probability that there will be 4 girls and 3 boys among the ticket holders, we need to use the hypergeometric distribution. The group of interest is the 17 students in the group, and the sample is the 7 tickets being raffled off.
The probability can be calculated using the formula:
P(X = k) = (C(n, k) * C(N-n, r-k)) / C(N, r)
Where:
P(X = k) is the probability of getting k girls and r-k boys,
C(n, k) is the combination of choosing k girls from n,
C(N-n, r-k) is the combination of choosing r-k boys from N-n,
C(N, r) is the combination of choosing r tickets from N, which is 17 in this case.
By substituting the given values, we have:
P(X = 4) = (C(8, 4) * C(17-8, 7-4)) / C(17, 7) = (70 * 42) / 19448 = 0.152
Therefore, the probability that there will be 4 girls and 3 boys among the ticket holders is 0.152 or 15.2%.