Probability of Randomly Selective Event, Conditional Probability

[conniebear14]

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]

 

[conniebear14]

it didn't post the numbers but the blanks correspond to 56% and 8% respectively

 

[LCKurtz]

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.

 

[conniebear14]

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?

 

[LCKurtz]

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...

 

[HallsofIvy]

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