Problem

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 three decimal places as needed.
A. 0.009
B. 0.169
C. 7.150
D. 0.013

Answer

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Answer

Final Answer: The probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating is approximately \(\boxed{0.009}\).

Steps

Step 1 :The problem is asking for the probability that all 11 graduates find a job in their chosen field within a year. This is a binomial probability problem where the probability of success (finding a job in their chosen field within a year) is 0.65 and the number of trials (the number of graduates) is 11. The probability of all 11 graduates finding a job in their chosen field within a year is simply the probability of success raised to the number of trials.

Step 2 :Let's denote the probability of success as \(p_{success} = 0.65\) and the number of trials as \(n_{trials} = 11\).

Step 3 :The probability is calculated as \(probability = p_{success}^{n_{trials}}\).

Step 4 :After calculating, we get \(probability = 0.008750783174008792\).

Step 5 :Rounding to three decimal places, we get \(probability = 0.009\).

Step 6 :Final Answer: The probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating is approximately \(\boxed{0.009}\).

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