12 of 13 Concepts completed (i) Fill in the Blank Question $20 \%$ of the patron's order the chef's special. The probability that 2 out of the next ten customers will order the chef's special is (round your answer to three decimal places). Need help? Review these concept resources. (1) Read About the Concept

Step 1 ：This is a binomial probability problem. The probability of success (ordering the chef's special) is 20% or 0.2. We want to find the probability of exactly 2 successes in 10 trials (customers).

Step 2 ：The formula for binomial probability is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where: \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) is the combination of n items taken k at a time, p is the probability of success, n is the number of trials, and k is the number of successes.

Step 3 ：We can plug in the values into the formula: n = 10, k = 2, p = 0.2, and calculate the result.

Step 4 ：The combination of 10 items taken 2 at a time is 45.

Step 5 ：The probability is calculated as \(P(X=2) = C(10, 2) * (0.2^2) * ((1-0.2)^(10-2)) = 0.302\).

Step 6 ：Final Answer: The probability that 2 out of the next ten customers will order the chef's special is \(\boxed{0.302}\).