Probability

[mrs1945]

I can't believe I have forgotten how to do this. My grandson always turns to me for help. His math problem is:

Norton was thinking of a two-digit counting number, and he asked Simon to guess the number. Describe how you can find the probability that Simon will guess correctly on the first try.

Can someone PLEASE help me out. He is patiently waiting on my phone call.

Mary

 

[tkhunny]

Sure! Count them.

10, 11, 12, ..., 99

How many are there?

 

[mrs1945]

I know the answer is 1/90. I do not know how to correctly "Describe how you can find the probability that Simon will guess correctly on the first try."

I assume the Event is: Guessing the 2-digit counting number
I assume the Event is (E)=1/90
I assume the Sample Space is (S)= 10,11,12,etc to 99


I have no idea how to show this. Please help!!

 

[tkhunny]

You didn't answer my question. 10, 11, ..., 99 How many in this list?

If there are three elements and each is equally probable, the probabiliy of selecting any one of them is 1/3

If there are 13 elements and each is equally probable, the probabiliy of selecting any one of them is 1/13

 

[mrs1945]

As previously stated, 10 thru 99 = 90 (number in the list).
Question was:
Norton was thinking of a two-digit counting number, and he asked Simon to guess the number. Describe how you can find the probability that Simon will guess correctly on the first try.
.........................................................................................................................
My answer is:
E={90}
S={90}
Number of possible outcomes in E is 1
and the number of possible outcomes in S is 90
Therefore, the probability of guessing the correct 2-digit number Norton is thinking of is P("90")=1/90
.........................................................................................................................
Is my answer the CORRECT WAY of "describing how you can find the probability that Simon will guess correctly on the first try."

 

[JeffM]

I seldom comment on probability because I studied it probably about the same time that you did, which was a long time ago.

tkhunny and galactus and subhotosh khan can answer your questions, but the former two usually comment late in the day, and you seem to be in a hurry. Royhaas seems to be the SUPER whiz at probability, but he comments only a few times a week. (This is a volunteer site; most of the volunteers have full time jobs, and no one is paid.)

Having warned you that I am nowhere close to an expert, I shall give an opinion only because you want to get back to your grandson as soon as possible.

First, in my opinion, you have the right answers. There are 90 possible outcomes, 10 for 10 through 19, 10 for 20 through 29, etc.
And, IF YOU ASSUME THAT EACH OF THESE OUTCOMES IS EQUALLY PROBABLE, the probability of each is then (1/90). This is classical-style probability thinking as it was developed in the 17th and 18th century. That is the logic of your answer and mine. And it will be understandable to a child. (Let's pray that we both remember enough to be correct.)

Second, if putting the answer in what is the currently preferred notation and vocabulary is the issue, you will have to wait until some volunteer who is au courant on that comes along. I am not and so will not venture even an opinion.

 

[tkhunny]

Second, if putting the answer in what is the currently preferred notation and vocabulary is the issue, you will have to wait until some volunteer who is au courant on that comes along. I am not and so will not venture even an opinion.

You are being very polite. "currently preferred notaion"

Other possibilities are demanded, esoteric, and others.

 

[JeffM]

You are being very polite. "currently preferred notaion"

Other possibilities are demanded, esoteric, and others.

I was being cautious, not polite. I noticed that you disapproved of my saying that the asymptote "was at x = 5" and preferred saying that the asymptote "was x = 5." Furthermore, what I remember about the foundations of probability theory as laid down in the twentieth century still makes my head hurt. I stopped getting developments in probability theory after the time of the Reverend Bayes. This is hardly surprising: I am so primitive that I still believe in infinitessimals (despite Bishop Berkeley).