In the United States, 40% of the population has brown eyes. Four United States r

Question

In the United States, 40% of the population has brown eyes. Four United States residents are surveyed at random. a) Use the multiplication rule to find the probability that first person surveyed has brown eyes and the last three don't. That is, find P(B & O & O & O), where B denotes a person with brown eyes and O denotes a person with not brown eyes. b) Begin with BOOO, make a complete list of all the different possible arrangements where one person has brown eyes and the other three don't. c) Based on the results from parts and a and b, what is the probability of getting exactly one person out of the four has brown eyes.

Explanation / Answer

here probabilty of brown eyes P(B) =0.4

and of other P(O) =1-0.4=0.6

a)hence P(B&O&O&O)=0.4*0.6*0.6*0.6=0.0864

b) list is

B O O O

O B O O

O O B O

O O O B

c)as there are 4 result of this kind

hence from a) and b) probability of one brown and 3 other =4*0.0864=0.3456

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