Q#1 Suppose a researcher goes to a small college of 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample of size n = 20 of the faculty. Let the random variable X represent the number of faculty in the sample of size n = 20 that have blood type O-negative. a)What is the probability that 3 of the faculty have blood type O-negative? b) What is the probability that at least one of the faculty has blood type O-negative? c)Find the probability distribution of the aculty have blood type O-negative d) also verify your result using Formula
+6250 Q#1 Suppose a researcher goes to a small college of 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample of size n = 20 of the faculty. Let the random variable X represent the number of faculty in the sample of size n = 20 that have blood type O-negative. a)What is the probability that 3 of the faculty have blood type O-negative? b) What is the probability that at least one of the faculty has blood type O-negative? c)Find the probability distribution of the aculty have blood type O-negative d) also verify your result using Formula
\(X \text{ is binomially distributed with parameters}\\ n=20,~p=\dfrac{12}{200}=\dfrac{3}{50}\)
\(P[X=3] = \dbinom{20}{3}\left(\dfrac{3}{50}\right)^3\left(\dfrac{47}{50}\right)^{17} = \\ \dfrac{41011174284214815703116854545293}{476837158203125000000000000000000} \approx 0.086\)
\(P[1 \leq X] = 1-P[X=0] = \\ 1-\left(\dfrac{47}{50}\right)^{20} = \\ \dfrac{6770074452100164190549251988657599}{9536743164062500000000000000000000} \approx 0.7099\)
I don't understand questions (c) and (d)
