Can a Probability Be Greater Than 1 in Statistics?

[new324]

Hello, I was wondering if someone could help me with a question my homework has invoked. In statistics, if a probability is greater than 1 would it just be equal to 1? The problem arose quite a few times when working with Discrete Random Variables.

For example, 80% of a 25 person survey is considered a success. The probability that more than 15 of the people will be a success is...

p(16)+p(17)+p(18)+p(19)+p(20)+p(21)+p(22)+p(23)+p(24)+p(25)

I worked this specific problem out with Minitab as instructed, and after summing the column that I stored the probabilities in it yielded 5.97511. Clearly, this seems wrong. I would think that the probability couldn't be greater than 1, or ever greater than .999999(repeating).

I also encountered the problem a few times when using the Appendix charts which we were asked to use to solve a few of the problems.

Thanks for any help.

 

[matt grime]

You probably worked it out wrongly. The probability of an event is a number between 0 and 1 inclusive.

 

[new324]

Okay, thank you. I don't guess you could help me work out the example I gave so I could see what I am doing wrong could you?

 

[new324]

Sorry, I figured it out. It seems I was using the wrong command in my calculator, and looking at the table wrong. Thanks again for letting me know that my assumption was correct, and that I was in fact making a mistake.

 

[HallsofIvy]

Okay, thank you. I don't guess you could help me work out the example I gave so I could see what I am doing wrong could you?

If you gave us the data you were working on, we might.

"For example, 80% of a 25 person survey is considered a success. The probability that more than 15 of the people will be a success is..."

Doesn't make sense. 80% of 25 is 20. I think that by "80% of a 25 person survey", you mean getting responsed from 80% of the people: 20 people. I don't know what you mean by "more than 15 of the people will be a success".

What you have calculated would be the probability of getting more than 15 people to respond to the survey IF the numbers you are using, P(16), P(17), etc. are the probabilities of exactly that number of people responding. I'm wondering if your P(16), etc. are not the probability of 16 or fewer people responding (i.e. the cumulative probability). That might account for you getting such a high answer. What, for example is P(25)?

 

[new324]

Well I appreciate the input, but as I stated I figured out my problem. But I figured I would go ahead and explain, I should have said SAMPLE survey rather than survey. It is known that 80% of the total population is a success. The question is what the probability is that the random sample survey of 25 people (out of the total population) would yield a more than 15 successus. Which would be the probability of 16 successes + the probability of 17 successes all the way up to 25.

 

[matt grime]

"It is known that 80% of the total population is a success"

Better to say that the probability of a 'success' is 80% rather than 80% of the population is a success.

 

[new324]

Understandable. I'll keep that in mind for all future references. Thank you.