Probability of Randomly Selective Event, Conditional Probability

In summary: For example, if p = 0.2, then the probability that none will buy is (1- 0.2)^5= (0.8)^5= 0.32768. Then the probability that "at least one" will buy is 1- 0.32768= 0.67232.
  • #1
conniebear14
9
0

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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  • #2
it didn't post the numbers but the blanks correspond to 56% and 8% respectively
 
  • #3
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.
 
  • #4
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?
 
  • #5
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...
 
  • #6
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
 

Related to Probability of Randomly Selective Event, Conditional Probability

What is the probability of a randomly selective event?

The probability of a randomly selective event is the likelihood that a specific outcome will occur when an event is chosen at random. This is typically expressed as a decimal or fraction between 0 and 1, where 0 represents no chance of the event occurring and 1 represents absolute certainty.

How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you roll a standard six-sided die, the probability of rolling a 3 would be 1/6, since there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling any number from 1 to 6).

What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. This is written as P(A|B), where A is the event of interest and B is the given condition. It is calculated by dividing the probability of both events occurring together by the probability of the given condition occurring.

What is the difference between independent and dependent events?

Independent events are events where the occurrence of one event does not affect the probability of the other event occurring. In contrast, dependent events are events where the occurrence of one event does affect the probability of the other event occurring. For example, if you draw a card from a deck and then draw another card without replacing the first one, these are dependent events because the probability of the second card being drawn is affected by the first card that was drawn.

How can probability be used in real life?

Probability is used in a variety of real-life situations, such as in weather forecasting, risk assessment, gambling, and insurance. It can also be used to make informed decisions, such as in business and finance, where the likelihood of different outcomes can be calculated to determine the best course of action.

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