Part A:
Given that 47% of adults prefer milk chocolate to dark
chocolate, for a random sample of n = 4 adults, the probability that all four adults say that they
prefer milk chocolate to dark chocolate is given by
[tex]P(4)=(0.47)^4=0.049[/tex]
Part B:
The probability that exactly two of the four adults
say they prefer milk chocolate to dark chocolate is given by
[tex]P(2)={ ^4C_2(0.47)^2(1-0.47)^2} \\ \\ =6(0.2209)(0.2809)=0.372[/tex]
Part C:
The probability that at least one adult prefers milk
chocolate to dark chocolate is given by
[tex]P(at \ least \ 1)=P(X\geq1) \\ \\ =P(1)+P(2)+P(3)+P(4) \\ \\ =1-P(0)=1-{ ^4C_0(0.47)^0(1-0.47)^4} \\ \\ =1-(0.53)^4=1-0.0789=0.921[/tex]
