In a certain state, it has been shown that only 56% of the high school graduates who are capable of college work actually enroll in colleges.Find the probability that, among the 11 capable high school graduates in this state, each number will enroll in college.

all 11

You're kidding, right? 11 capable graduates in the whole state?

Anyway, just work it out:
P(1) = .56
P(2) = .56*.56 = .56^2
...
P(11) = ?

To find the probability that all 11 capable high school graduates will enroll in college, we need to multiply the individual probabilities of each student enrolling in college.

Given that only 56% of capable high school graduates enroll in college, the probability that one capable high school graduate will enroll in college is 0.56.

Since the probability is the same for each student, we can use the multiplication rule of probability.

Probability of all 11 capable high school graduates enrolling in college:
P(11 students enrolling) = (0.56) * (0.56) * (0.56) * ... * (0.56) (11 times)

P(11 students enrolling) = (0.56)^11

Calculating this probability:
P(11 students enrolling) = 0.00804617

Therefore, the probability that all 11 capable high school graduates will enroll in college is approximately 0.00804617, or 0.804617%

To find the probability that all 11 capable high school graduates will enroll in college, you need to multiply the probabilities of each individual enrolling.

Given that only 56% of capable high school graduates enroll in college, the probability of one individual enrolling is 0.56 (or 56%).

To find the probability that all 11 individuals enroll, you multiply this probability 11 times:

P(enrolling) = P(enrolling for the first individual) * P(enrolling for the second individual) * ... * P(enrolling for the eleventh individual)

P(enrolling) = 0.56 * 0.56 * 0.56 * ... (11 times)

Mathematically, this can be represented as:

P(enrolling) = 0.56^11

Calculating this value will give you the probability that all 11 capable high school graduates will enroll in college.