It has been estimated that the proportion of people in the United States having

Question

It has been estimated that the proportion of people in the United States having type O blood is 0.40. Imagine that a large metropolitan hospital has a list of several thousand people willing to donate blood. If three people are selected at random, what are the probabilities that:

(a) None of the three has type O blood

(b) Only one has type O blood

(c) Two have type O blood

(d) All three have type O blood

What is the sum of the four probabilities estimated in the previous problem? Does the result make sense? Why or why not?

Explanation / Answer

P(O blood group) = 0.4

a)

P( no one has O blood group) = 0.6*0.6*0.6 = 0.216

b)

P(one has type O) = 3*0.4*0.6*0.6 = 0.432

c)

P(two have type O) = 3*0.4*0.4*0.6 = 0.288

d)

P(all have type O) = 0.4*0.4*0.4 = 0.064

Sum of all = 1

Yes as the sum of all the possibilities is 1

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