Question

A real estate agent has 17 properties that she shows. She feels that there is a 40% 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 6 properties in one week. Round your answer to four decimal places.

Answer 1

Solution:

Given,

p = 40% = 0.4

1 - p = 1 - 0.4 = 0.6

n = 17

X follows the Binomial(17 , 0.4)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

Now ,

P(Less than 6  properties )

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

= (₁₇ C ₀) * 0.4⁰ * (0.6)^{17 - 0}  + (₁₇ C ₁) * 0.4¹ * (0.6)^{17 - 1}  + (₁₇ C ₂) * 0.4² * (0.6)^{17 - 2}  + (₁₇ C ₃) * 0.4³ * (0.6)^{17 - 3} + (₁₇ C ₄) * 0.4⁴ * (0.6)^{17 - 4} + (₁₇ C ₅) * 0.4⁵ * (0.6)^{17 - 5}  

= 0.00016926659 + 0.00191835474 + 0.01023122526 + 0.03410408421 + 0.0795761965 + 0.13793207393

= 0.2639