What is the Probability of Selling 8 Listings Out of 10?

[maiad]

Homework Statement

You are a real estate salesperson and you currently have 10 listings. Past experience has shown that you will sell approximately 70% of your listings. If sales are independent:

What is the probability that you make exactly 8 sales?

Homework Equations

The Attempt at a Solution

I was wondering why 70% would be used as the the probability for the event of interest... I thought the probability would be the probability of ONE listing that would sell and not 7/10 of your listings. Can someone explain?

 

[Ray Vickson]

Homework Statement

You are a real estate salesperson and you currently have 10 listings. Past experience has shown that you will sell approximately 70% of your listings. If sales are independent:

What is the probability that you make exactly 8 sales?

Homework Equations

The Attempt at a Solution

I was wondering why 70% would be used as the the probability for the event of interest... I thought the probability would be the probability of ONE listing that would sell and not 7/10 of your listings. Can someone explain?

The 70% figure is a long-run average. It really means that the probability of sales is 0.70 per listed property.

Sometimes problem posers want to sound more conversational and less formal, so instead of saying p = 0.7 per trial they say there is a 70% chance per trial, or sales = 70% of listings; that means 70% on average, not in any individual group of listings.

 

[haruspex]

I think there's a little more to it than conversational usage. It is saying that your experience is that you sell 70% of your listings. That's a simple observation. From that you infer that your probability of selling a given listing (in the future) is 0.7. There are certain assumptions in that inference which might not in general be valid.