People with O-negative blood are called \"universal donors\" because O-negative

Question

People with O-negative blood are called "universal donors" because O-negative blood can be given to anyone else, regardless of the recipient's blood type. Only about 6% of people have O-negative blood. If donors line up at random for a blood drive,

(a) How many do you expect to examine before you find someone who has O-negative blood?

(b) What's the probability that the first O-negative donor found is one of the first four people in line?

c) What's the probability that the third O-negative donor found is the tenth in line?

Explanation / Answer

a)
Expected number of people to be examined = 1/p = 1/0.06 = 16.6667

b)
P(X = 1) = 4C1 * 0.06 * 0.94^3 = 0.1993

c)
First 2 O -ve should be among first 9
P(X = 2) = 9C2 * 0.06^2 * 0.94^7 = 0.084

Now we need probability of 10 person with O -ve
Required probability = 0.084 * 0.06 = 0.005

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