+0

# 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 s

0
686
1
+82

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
+17711
+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
Sort:

#1
+17711
+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

### 5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details