SOLUTION: Use the following information below to answer the next two questions. In a particular town, 30% of all adults have brown hair. 18. If three adults are randomly and independen

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Question 1119555: Use the following information below to answer the next two questions.
In a particular town, 30% of all adults have brown hair.
18. If three adults are randomly and independently selected for a survey, calculate the probability that all three have brown hair.
(a) 0.300
(b) 0.027
(c) 0.090
(d) 0.900
19. If two adults are randomly and independently selected for a survey, calculate the probability that at least one has brown hair.
(a) 0.49
(b) 0.51
(c) 0.70
(d) 0.39

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
this looks like a binomial distribution type of problem.

p = .3 equals probability that a person has brown hair.
q = 1 - p = .7 equsls probability that a person doesn't have brown hair.

the formula is p(x) = c(n,x) * p^2 * q^(n-x)

in the first problem, n = 3 and you are looking for the probability that all 3 have brown hair.

formula becomes p(3) = .3^3 * .7^0 * c(3,3).

this is equal to .027 * 1 * 1 = .027

that would be selection b.

in the second problem, n = 2 and you are looking for the probability that at least 1 has brown hair.

that would be equal to 1 minus the probability that all 2 do not have brown hair.

formula becomes p(0) = .3^0 * .7^2 * c(2,0).

this is equal to 1 * .49* 1 = .49

that's the probability that none have brown hair.

the probability that at least 1 has brown hair would be 1 minus .49 = .51

that would be selection b.

the complete probabilities should always add up to 1.

those complete probabilities are shown in the following excel printout.