To calculate the probability that 8 out of 10 students will graduate, we need to use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where:
- n is the total number of trials (in this case, the number of students)
- k is the number of successful trials (in this case, the number of students who graduate)
- p is the probability of success (in this case, the probability that a student will graduate)
Assuming that the probability of a student graduating is 0.8 (or 80%), we can plug in the values for n, k, and p:
P(X = 8) = (10 choose 8) * 0.8^8 * (1 - 0.8)^(10 - 8)
P(X = 8) = 45 * 0.16777 * 0.01024
P(X = 8) = 0.076
Therefore, the probability that 8 out of 10 students will graduate is approximately 0.076, or 7.6%.