Question

Destination Weddings Twenty-six percent of couples who plan to marry this year are planning destration weddings. Assume the vanabi random sample of 4 couples who plan to marry, find the probability of the following Round intermediate calculations and final answers to three decimal places Exactly 2 couples will have a destination wedding

Answer 1

Using the binomial probability formula, the probability that exactly 2 out of 4 couples are planning a destination wedding, given a 26% chance for each couple, is approximately 22.2%.

Step-by-step explanation:

The question asks for the probability that exactly 2 out of 4 randomly selected couples are planning destination weddings, given that 26% of couples are planning such weddings. This can be modeled using the binomial probability formula:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Where:

• n = total number of couples (n=4)
• k = number of couples with a destination wedding (k=2)
• p = probability of a couple planning a destination wedding (p=0.26)
• C(n,k) = binomial coefficient

Using the formula, we calculate:

C(4,2) * 0.26^2 * (1-0.26)^(4-2) = 6 * 0.0676 * 0.5476 ≈ 0.222

The probability that exactly 2 out of 4 couples are planning a destination wedding is therefore approximately 0.222, or 22.2% when rounded to three decimal places.