Answer to Question #264376 in Statistics and Probability for Maria

Question

 A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5

randomly selected graduates, at least one finds a job in his or her chosen field within a

year of graduating. Round your answer to the nearest thousandth. 

Answer 1

n = 5

p = 0.62

(1 - p) = 0.38

As per binomial distribution formula

$P(X = x) = C^n_x \times p^x \times (1 - p)^{n - x}$

We need to calculate P(X ≥ 1)

$P(X ≥ 1) = P(X=1) + P(X=2) + P(X=3) + P(X=4) +P(X=5) \\ P(X ≥ 1) = (C^5_1 \times 0.62^1 \times 0.38^4) + (C^5_2 \times 0.62^2 \times 0.38^3) + (C^5_3 \times 0.62^3 \times 0.38^2) + (C^5_4 \times 0.62^4 \times 0.38^1) + (C^5_5 \times 0.62^5 \times 0.38^0) \\ P(X ≥ 1) = 0.065 + 0.211 + 0.344 + 0.281 + 0.092 \\ P(X ≥ 1) = 0.993$