Question

Last week, a flower delivery business conducted a survey on customer happiness. They found that 27% of their customers were "pleased" with the service.  If the company surveys 2 of their customers the next week, what is the probability that exactly 2 are pleased? Write to the nearest 1000th Responses

Answer 1

The probability that exactly 2 out of 2 customers surveyed next week are pleased is 0.073, after using the binomial probability formula with n=2, k=2, and p=0.27.

Step-by-step explanation:

To calculate the probability that exactly 2 customers are pleased with the service, when the probability of one customer being pleased is 27%, we use the binomial probability formula:

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

Where:

• n is the number of trials (in this case, 2 customers)
• k is the number of successes (in this case, 2 pleased customers)
• p is the probability of success on a single trial (27% or 0.27)

We are looking for the probability that k = 2 (both customers are pleased). So the formula for this problem is:

P(X = 2) = (2 choose 2) * 0.27^2 * (1-0.27)^(2-2)

Calculations:

• (2 choose 2) = 1
• 0.27^2 = 0.0729
• (1-0.27)^(2-2) = 1

So, P(X = 2) = 1 * 0.0729 * 1, which equals 0.0729 or 0.073 when rounded to the nearest thousandth.

Therefore, the probability that exactly 2 out of 2 customers surveyed next week are pleased is 0.073, to the nearest thousandth.