3131% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.
Accepted Solution
A:
Answer:a) 0.23235b) 0.53806c) 0.22959Step-by-step explanation:Given-Adults having cashews as their favorite kind of nut [tex]= 0.31[/tex]Adults not having cashews as their favorite kind of nut [tex]= 1-0.31\\= 0.69[/tex]a) Exactly three[tex]\frac{12}{3} * (0.31)^3* (0.69)^9\\= 0.23235[/tex]Thus, the probability that three adults have cashews as are their favorite nut is 0.23235b) at least four[tex]1-P(1)-P(2)-P(3)\\[/tex][tex]1-[({\frac{12}{1} * (0.31)^1* (0.69)^{11})+({\frac{12}{2} * (0.31)^2* (0.69)^{10})+({\frac{12}{3} * (0.31)^3* (0.69)^{9})][/tex][tex]=0.53806[/tex]c) at most two[tex]({\frac{12}{1} * (0.31)^1* (0.69)^{11})+({\frac{12}{2} * (0.31)^2* (0.69)^{10})\\= 0.22959[/tex]