Despite reports that dark chocolate is beneficial to the heart, suppose that 47%

Question

Despite reports that dark chocolate is beneficial to the heart, suppose that 47% of adults still prefer milk chocolate to dark chocolate. Suppose a random sample of n = 4 adults is selected and asked whether they prefer milk chocolate to dark chocolate. (Round your answers to three decimal places.)

(a) What is the probability that all four adults say that they prefer milk chocolate to dark chocolate?

(b) What is the probability that exactly two of the four adults say they prefer milk chocolate to dark chocolate?

(c) What is the probability that at least one adult prefers milk chocolate to dark chocolate?

Explanation / Answer

this is a binomial distribution and P= 0.47 q= 0.53

a) P x=4 : (4C4)*(0.47)^(4) *(0.53)^(0) =0.0487

a) P x=2 : (4C2)*(0.47)^(2) *(0.53)^(2) =0.3723

c) at last one adult prefers milk chocolate

1-P(x=0) =1- (4C0)*(0.47)^(0) *(0.53)^(4)=1- 0.0789=0.9211

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