What Are the Probabilities Linked to Business and Financial Media Consumption?

[mouse]

hi,

need some help on these stats problems that i am confused about?

1. market research in a particular city indicated that during a week 18% of all adults watched a television program oriented to business and financial issues,
12% read a publication oriented to these issues, and 10% do both.

(a) what is the probability that an adult i this city who watches a television program oriented to business and financial issues reads a publication oriented to these issues?

(b) what is the probability that an adult in this city who reads a publication orientated to buiseness and financial issues watches television program oriented to these issues?

2. a conference began at noon with two parallel sessions. the session on portfolio management was attended by 40% of the delegates, while the session on chartism was attended by 50%. the evening session consisted of aa talk titled, "is the random walk dead?" this was attended by 80% of all delegates.

(a) if attendance at the sessions on portfolio management and chartism are mutually exclusive, what is the probability that a randimly chosen delegate attended at least one of these sessions?

(b) if attendance at the portfolio management and evening sessions are statistically independent, what is the probability that a randomly chosen delegate attended at leaset one of these sessions?

(c) of those attending the chartism session, 73% also attended the evening session. what is the probability that a randomly chosen delegate attended at least one of these two sessions?

3. a lawn - care service makes telephone solitications, seeking customers for the coming season. a review of the records indicated that 15% of these solitications produced new customers, adn that of these new customers, 80% had used some rival service the presious year. it was also estimated that all solitication calls made, 60% were to people who had used a rival service the previous year. what is the probabiltity that a call to a person who used a rival service the previous year will produce a new customer for the lawn-care serice?

thanks

 

[H_man]

Hi Mouse,

I could just tell you the answer but its better if I explain the idea to you...

The best way to get moving on these problems is to draw a diagram to help you see what's going in.

i) In the case of question one you can draw a rectangle to represent all the population of the city.

ii) Now add to the rectangle a bubble which fills approximately 18% of the rectangle.

iii) Now add a second bubble inside the rectangle this time taking up 12% of the space BUT at the same time overlapping the first bubble. The overlap between the two bubbles represents the 10% who both watch TV and read the magazine.

Now question 1i) asks what is the chance that someone who ALREADY watches the TV prog ALSO reads the magazine. So these people are represented by this first bubble!

Now what is the percent of people in the first bubble who read the Mag... This is your answer!

An identical procedure is followed to solve the next part.

 

[quicknote]

Hi there,

I would be happy to help you with these stats problems. Let's take a look at each of them individually:

1. For the first problem, we can use the information given to calculate the probability of an adult in this city who watches a television program oriented to business and financial issues also reading a publication oriented to these issues. We know that 18% of adults watch the program and 10% do both, so the probability would be 10% / 18% = 0.556 or 55.6%. Similarly, for an adult who reads the publication, the probability of also watching the program would be 10% / 12% = 0.833 or 83.3%.

2. For this problem, we need to use the information given to calculate the probability of a randomly chosen delegate attending at least one of the sessions. Since attendance at the sessions on portfolio management and chartism are mutually exclusive, we can simply add their probabilities to get the total probability of attending at least one of these sessions. So the probability would be 40% + 50% = 90%. For the second part, if the attendance at the portfolio management and evening sessions are statistically independent, we can use the multiplication rule to calculate the probability. So it would be 40% * 80% = 32%. Finally, for the third part, we can use the information given to calculate the probability of a delegate attending at least one of these two sessions. We know that 73% of those who attended the chartism session also attended the evening session, so the probability would be 40% + (50% * 73%) = 77.5%.

3. For the final problem, we can use the information given to calculate the probability of a call to a person who used a rival service the previous year producing a new customer for the lawn-care service. We know that 15% of solicitations produced new customers and that of these new customers, 80% had used a rival service the previous year. So the probability would be 15% * 80% = 12%.

I hope this helps! Let me know if you have any further questions or need clarification on any of the solutions. Good luck with your research!