The probability that all 12 students stay in school and graduate is approximately 0.000003.
To find the probability that all 12 students stay in school and graduate, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Where:
n = number of trials (12 in this case)
k = number of successes (all 12 staying in school and graduating)
p = probability of success (probability of a student staying in school and graduating)
In this case, the probability of a student staying in school and graduating is given as 10.7%, which can be written as 0.107.
P(all 12 stay in school and graduate) = (12 choose 12) * 0.107^12 * (1 - 0.107)^(12 - 12)
Calculating the probability:
P(all 12 stay in school and graduate) = 1 * 0.107^12 * 0.893^0
P(all 12 stay in school and graduate) ≈ 0.107^12 ≈ 0.000003
Therefore, the probability that all 12 students stay in school and graduate is approximately 0.000003.