SOLUTION: A real estate agent has 15 properties that she shows. She feels there is a 50% chance of selling any one property during a week. The chance of selling any one property is indepen

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Question 1145496: A real estate agent has 15 properties that she shows. She feels 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 4 properties in one week.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Selling "less than 4 properties" means selling either 3, 2, 1, or 0 properties.

Probability of selling exactly 3 properties in one week: %280.5%29%5E3+%2A+%280.5%29%5E12+%2A+%2815%21%2F%283%21%2A12%21%29%29 = 0.0139
Probability of selling exactly 2 properties in one week: %280.5%29%5E2+%2A+%280.5%29%5E13+%2A+%2815%21%2F%282%21%2A13%21%29%29 = 0.0032
Probability of selling exactly 1 property in one week: %280.5%29%5E1+%2A+%280.5%29%5E14+%2A+%2815%21%2F%281%21%2A14%21%29%29 = 0.0005
Probability of selling exactly 0 properties in one week: %280.5%29%5E15 = 0.00003

Probability of selling "less than 4 properties": 0.0139 + 0.0032 + 0.0005 + 0.00003 = 0.01763