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# Real Estate: Conflict and Conflict in Selling Houses

A real estate agent has four houses to sell before the end of the month by contracting prospective customers one by one. Each customer has an independent 0.24 probability of buying a house on being contacted by the agent.

a. If the agent has enough time to contact only 15 customers, how conflict can she be of selling all four houses within the available time?

b. If the agent wants to be at least 70% confident of selling all the houses within the available time, at least how many customers should she contact?

c. What minimum value of p will yield 70% confidence for selling all four houses by contacting at most 15 customers?

#### Solution Preview

a. If the agent has enough time to contact only 15 customers, how conflict can she be of selling all four houses within the available time?

This is a binomial distribution with p=0.24 and n=15. What we need to calculate the probability of x being greater than or equal to zero.
P(x>=4) = 1- P(x<4) = 1-P(x=0)-P(x=1)-P(x=2)-P(x=3)
=1-COMBIN(15,0)*0.24^0*0.76^15-COMBIN(15,1)*0.24^1*0.76^14-COMBIN(15,2)*0.24^2*0.76^13 -COMBIN(15,3)*0.24^3*0.76^12
=0.50223842

Where CONBIN(15,0) is the combination for 0 successes in 15 trials.
She will be 50.22% confident that all the four houses ...

#### Solution Summary

This is a probability question on the real estate market.

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