Question

40% of couples who plan to get married this year are planning destination weddings. In a random sample of 12 couples who plan to marry, find the probability that
a) exactly 6 couples will have a destination wedding
b) at least 2 couples will have a destination wedding
c) fewer than 3 couples will have a destination wedding

Answer 1

Question # 12024

$40\%$ of couples who plan to get married this year are planning destination weddings. In a random sample of 12 couples who plan to marry, find the probability that a) exactly 6 couples will have a destination wedding b) at least 2 couples will have a destination wedding c) fewer than 3 couples will have a destination wedding

Solution. The condition implies that the probability of a destination wedding in a randomly selected couple equals 0.4. Denote by $N$ the number of couples of those 12 that plan to have a destination wedding. Hence, we are to find:

1) $P(N=6)=C_{12}^{6}0.4^{6}\cdot 0.6^{6}\approx 0.17$.

2) $P(N\geq 2)=1-P(N=1)-P(N=0)=1-C_{12}^{1}0.4\cdot 0.6^{11}-0.6^{12}\approx 0.98$.

3) $P(N\leq 3)=0.6^{12}+C_{12}^{1}0.4^{1}0.6^{12}+C_{12}^{2}0.4^{2}0.6^{10}+C_{12}^{3}0.4^{3}0.6^{9}\approx 0.22$