Question

A real estate agent has 15 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 44 properties in one week. Round your answer to four decimal places.

Answer 1

0.0176

Explanation:

This is binomial distribution probability with formula:

`P(x=r)=nCr*p^r *(1-p)^(n-r)`

Where

n is the total number of trials [here 15 properties]

p is probabilty of success, sell [p = 0.5]

r is what we want [here we want probability of selling less than 4 properties, so r = 4]

Less than 4 means r<4, which means r = 0, r=1, r=2, r=3

We use the formula above and put in 4 different values of r and sum up the result. We will use a binomial calculator online to make it easy. So:

`P(x=0)=15C0*(0.5)^0 *(1-0.5)^(15-0)` +

`P(x=1)=15C1*(0.5)^1 *(1-0.5)^(15-1)` +

`P(x=2)=15C2*(0.5)^2 *(1-0.5)^(15-2)` +

`P(x=3)=15C3*(0.5)^3 *(1-0.5)^(15-3)`

This is equal to 0.0176