Question

A real estate agent has 18 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling less than 5 properties in one week. PART A (5 points): In your own words, explain how to create an accurate probability statement for this situation. PART B (5 points): Write the problem's probability statement using proper notation. PART C (10 points): Calculate the probability and round it to 4 decimal places.

Answer 1

An accurate probability statement for the situation, the binomial probability formula can be used, will get probability = 0.0004 (upto 4 decimal places).

Step-by-step explanation:

For this situation, we can use the binomial probability formula to calculate the probability of selling less than 5 properties in one week.

To create an probability statement, we can use the notation P(X < 5), where X represents the number of properties sold in a week.

To calculate the probability, we need to sum the probabilities of selling 0, 1, 2, 3, and 4 properties.

The probability of selling any one property is 50% or 0.5.

The probability of not selling any property is 1 - 0.5 = 0.5.

We can use the binomial probability formula P(X=k) = nCk * p^k * (1-p)^(n-k) to calculate the probabilities for each outcome.

=> P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

=> P(X < 5) = 18C0 * (0.5)^0 * (0.5)^(18-0) + 18C1 * (0.5)^1 * (0.5)^(18-1) + 18C2 * (0.5)^2 * (0.5)^(18-2) + 18C3 * (0.5)^3 * (0.5)^(18-3) + 18C4 * (0.5)^4 * (0.5)^(18-4)

= 0.0004.