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

In summary: For example, it assumes that the listings you have now are similar to those you've had in the past, and that the market conditions are similar. It probably assumes a bunch of other things too. But it's a reasonable starting point.In summary, the conversation discusses a real estate salesperson with 10 listings who has a past experience of selling 70% of their listings. The question posed is what is the probability of making exactly 8 sales if sales are independent. The 70% figure represents a long-run average and is used to infer a probability of 0.7 for selling a listing in the future. However, there are certain assumptions that need to be considered in this inference.
  • #1
maiad
102
0

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?
 
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  • #2
maiad said:

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.
 
  • #3
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.
 

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

What is a binomial probability distribution?

A binomial probability distribution is a type of probability distribution that describes the likelihood of obtaining a certain number of successes in a fixed number of independent trials. It is used in situations where there are only two possible outcomes for each trial, such as success or failure.

How is the binomial probability formula calculated?

The binomial probability formula is calculated using the following formula: P(x) = (nCx)(p^x)(q^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1-p).

What is the difference between a binomial probability and a normal distribution?

The main difference between a binomial probability and a normal distribution is that a binomial distribution is discrete while a normal distribution is continuous. This means that a binomial distribution can only take on certain values, while a normal distribution can take on any value on a continuous scale.

How can binomial probabilities be used in real life?

Binomial probabilities can be used in a variety of real-life situations, such as in quality control, market research, and medical studies. For example, a company may use binomial probabilities to determine the success rate of a new product, while a doctor may use binomial probabilities to determine the effectiveness of a new treatment.

What is the significance of the mean and standard deviation in a binomial distribution?

The mean and standard deviation in a binomial distribution provide important information about the distribution's shape and spread. The mean represents the expected number of successes in a given number of trials, while the standard deviation measures the variability in the number of successes. These values can be used to make predictions and analyze the data in a binomial distribution.

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