Probability of Randomly Selective Event, Conditional Probability

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Homework Help Overview

The discussion revolves around a probability problem related to a company's television advertisement and its impact on product purchases. The problem involves calculating the probability of an individual buying a product based on whether they have seen the advertisement, as well as determining the probability of at least one purchase among a group of five individuals.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the probabilities associated with purchasing the product based on advertisement exposure, with some noting the specific probabilities of 56% and 8% for different scenarios. There is confusion regarding the application of these probabilities to part B of the problem, particularly concerning the independence of events and the use of the binomial distribution.

Discussion Status

Some participants have successfully calculated the probability of an individual making a purchase, while others are exploring how to apply this to the scenario of multiple individuals. Guidance has been offered regarding the calculation of the probability that none of the individuals buy the product, suggesting a method involving the complement of the purchase probability.

Contextual Notes

There is mention of a specific homework equation related to conditional probability, and participants are navigating the implications of the independence of events in their calculations. The original poster has indicated uncertainty about how to proceed with part B, particularly in relation to the group of five individuals.

conniebear14
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Homework Statement



A company has been running a television advertisement for one of its new products. A survey was conducted. Based on its results, it was concluded that an individual buys the product with probability https://utdvpn.utdallas.edu/wwtmp/equations/42/,DanaInfo=.aevnhvE00ljvwm5Ntt.,SSL+b76747aa0afb1816e5979c66ce77851.png , if he/she saw the advertisement, and buys with probability https://utdvpn.utdallas.edu/wwtmp/equations/1e/,DanaInfo=.aevnhvE00ljvwm5Ntt.,SSL+e895ee9ca85bcbf1e55a96a7573c291.png , if he/she did not see it. Twenty-five percent of people saw the advertisement.

a. What is the probability that a randomly selected individual will buy the new product?
b. What is the probability that at least one of randomly selected five individuals will buy the new product?

Homework Equations


P(A|B) = P(B|A)P(A)/P(B)

The Attempt at a Solution


I already got part A correct.
The answer is .2
I am confused on part B probably because of the 1/5 thing. Which equation should I use and where should I start with this one?[/B]
 
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it didn't post the numbers but the blanks correspond to 56% and 8% respectively
 
You have the probability a given person buys is ##.2##. What is the probability they all fail to buy? You could use the binomial distribution but it is easy enough to just calculate.
 
LCKurtz said:
You have the probability a given person buys is ##.2##. What is the probability they all fail to buy? You could use the binomial distribution but it is easy enough to just calculate.
Okay so I calculated probability person does not buy as .8 from (1-.56)(.25) + (.92)(.75). But now I am stuck. Where does the five part come in? What should I do next?
 
If the probability the first person doesn't buy is ##.8##, and if they are independent, what is the probability the next person doesn't buy? So...
 
conniebear14 said:

Homework Statement



A company has been running a television advertisement for one of its new products. A survey was conducted. Based on its results, it was concluded that an individual buys the product with probability 58%, if he/she saw the advertisement, and buys with probability 8% if he/she did not see it. Twenty-five percent of people saw the advertisement.

a. What is the probability that a randomly selected individual will buy the new product?
b. What is the probability that at least one of randomly selected five individuals will buy the new product?

Homework Equations


P(A|B) = P(B|A)P(A)/P(B)

The Attempt at a Solution


I already got part A correct.
The answer is .2
I am confused on part B probably because of the 1/5 thing. Which equation should I use and where should I start with this one?[/B]
If the answer to (a), which you say you got, is p, then the probability that "at least one" will buy is the 1 minus the probability none will buy. The probability that none will buy is (1- p)^5
 

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