Suppose a researcher goes to a small college with 200 faculty members, 12 of which have blood type O-negative. She obtains a simple random sample of 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 0-negative.

a. What is the probability that 3 of the faculty have type O-negative?

b. What is the probability that at least one of the faculty has blood type O-negative?

yuhki
Nov 21, 2014

#1**+5 **

a) The probability of randomly choosing someone with blood type O-negative is 12/200.

The probability of randomly choosing someone without blood type O-negative is 188/200.

The probability of randomly choosing three type-O and seventeen non-type-O is:

(12/200)^3 x (188/200)^17 x the number of ways that this can occur.

Since the order in which these are chosen is unimportant, it is a combination, so we been the combination of choosing three out of twenty: 20nCr3

Our probabiltiy has become: 20nCr3 x (12/200)^3 x (188/200)^17 = 0.086 (approx.)

b) "At least one" means "one or more", so the easiest way is to find the probability that none have type O- negative blood and subtract this from 1.000.

The probability that none has type O-negative blood is: 20nCr0 x (12/200)^0 x (188/200)^20 = 0.290

Subtracting this from 1.000 gives a probability of 0.710.

geno3141
Nov 22, 2014

#1**+5 **

Best Answer

a) The probability of randomly choosing someone with blood type O-negative is 12/200.

The probability of randomly choosing someone without blood type O-negative is 188/200.

The probability of randomly choosing three type-O and seventeen non-type-O is:

(12/200)^3 x (188/200)^17 x the number of ways that this can occur.

Since the order in which these are chosen is unimportant, it is a combination, so we been the combination of choosing three out of twenty: 20nCr3

Our probabiltiy has become: 20nCr3 x (12/200)^3 x (188/200)^17 = 0.086 (approx.)

b) "At least one" means "one or more", so the easiest way is to find the probability that none have type O- negative blood and subtract this from 1.000.

The probability that none has type O-negative blood is: 20nCr0 x (12/200)^0 x (188/200)^20 = 0.290

Subtracting this from 1.000 gives a probability of 0.710.

geno3141
Nov 22, 2014