Question

A real estate agent has 12 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 at least 5 properties in one week. Round your answer to four decimal places.

Answer 1

Binomial Probability = ⁿC_x * (p)^x * (q)^n-x, where n = number of trials and x is the number of successes.

Here n = 12, p = 0.4, q = 1 – p = 0.6.

To Find P(X at least 5) = P(X 5) = P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)

P(X = 5) = ¹²C₅ * (0.4)⁵ * (0.6)^12-5 = 0.2270

P(X = 6) = ¹²C₆ * (0.4)⁶ * (0.6)^12-6 = 0.1766

P(X = 7) = ¹²C₇ * (0.4)⁷ * (0.6)^12-7 = 0.1009

P(X = 8) = ¹²C₈ * (0.4)⁸ * (0.6)^12-8 = 0.0420

P(X = 9) = ¹²C₉ * (0.4)⁹ * (0.6)^12-9 = 0.0125

P(X = 10) = ¹²C₁₀ * (0.4)¹⁰ * (0.6)^12-10 = 0.0025

P(X = 11) = ¹²C₁₁ * (0.4)¹¹ * (0.6)^12-11 = 0.0003

P(X = 12) = ¹²C₁₂ * (0.4)¹² * (0.6)^12-12 = 0.0002

Therefore P(X 5) = 0.2270 + 0.1766 + 0.1009 + 0.0420 + 0.0125 + 0.0025 + 0.0003 + 0.0002 = 0.5620

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The same can be found using the excel formula 1 - [BINOMDIST(4,12,0.4, TRUE)]

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