Question

A survey found that 68% of adults ages 18 to 25 thunk that their generation is unique and distinct.
a) If we randomly select 12 adult ages 18 to 25, what is the probability that exactly 4 of them think their generation is not unique and distinct?
b) If we randomly select 16 adults ages 18 to 25, what is the probability that more than 14 of them think their generation is unique and distinct?
c) If we randomly select 20 adults ages 18 to 25, what is the probability that at least 2 of them think their generation is not unique and distinct?

Answer 1

$(a)P(x=4)=C_{4}^{12}(0.32)^{4}(0.68)^{12-4}\approx 0.237\\ (b)P(x>14)=P(x=15)+P(x=16)\\ =C_{15}^{16}(0.68)^{15}(0.32)^{16-15}+C_{16}^{16}(0.68)^{16}(0.32)^{16-16}\\ \approx 0.0178\\ (c)P(x\geq 2)=1-P(x<2)\\ =1-[P(x=0)+P(x=1)]\\ =1-[C_{0}^{20}(0.32)^{0}(0.68)^{20-0}\\+C_{1}^{20}(0.32)^{1}(0.68)^{20-1}]\\ \approx 0.995 \\$