Find the indicated probability.
-A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 11 randomly selected graduates all find jobs in their
Chosen field within a year of graduating. Round to the nearest thousandth if necessary.
A) 0.169
B) 0.009
C) 0.013
D) 7.150

Question

Quizplus · Accepted Answer

This problem involves calculating the probability of a success (finding a job in their chosen field within a year) in a binomial distribution (either they find a job or they don't). The formula for this probability is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the total number of trials, k is the number of success, p is the probability of success, and (n choose k) is the binomial coefficient (the number of ways to choose k from n).

In this case, n = 11, k = 11, p = 0.65, and (n choose k) = 1 (there's only one way to choose all 11 graduates to find a job). Plugging these values into the formula, we get:

P(X = 11) = (11 choose 11) * 0.65^11 * (1-0.65)^(11-11)
P(X = 11) = 1 * 0.65^11 * 0.35^0
P(X = 11) = 0.009205 (rounded to the nearest thousandth)

Therefore, the closest answer choice is B: 0.009.

Find the Indicated Probability