Question

Twenty-six percent of couples who plan to marry this year are planning destination weddings. Assume the variable is binomial. In a random sample of 10 couples who plan to marry, find the probability of the following. Round the answers to four decimal places.  Source: Time magazine. 

 Exactly 5 couples will have a destination wedding 

 P (exactly 5 couples will have a destination wedding) = _______ 

Answer 1

Let denotes the number of couples out of 10 randomly selected who are planning destination weddings.

Assume, $X\sim Binomial (n=10, p=0.26)$

, where is the probability that a randomly selected couple is planning destination wedding.

Then, the probability that exactly 5 couples will have destination wedding is

   $P(X=5)=\binom{10}{5}\times0.26^5\times(1-0.26)^{10-5}$

$=252\times0.26^5\times0.74^5$

$=0.0664$