mathematical expectation

Mar 2010
110
0
Jerome parks downtown in front of the barber shop. The meter is expired and takes only quarters. Jerome looks in the barber shop to see how many customers are waiting. He understands that if the meter man comes along and notices his car parked by an expired meter, he will receive a ticket that will cost $10. He thinks for a moment and decides not to insert a quarter in the meter. What does this tell us about his estimate of the probability that a meter man will come by while he is in the barber shop? Your answer must complete the following sentence and you must justify your answer.

The probability of the meter man coming by is (more or less) than (a fraction inserted here).


I know this has to do with mathematical expectation and I know how to compute ME from all of my other hw questions, but I do not know where to start on this one...can somebody please help me out!
 

mr fantastic

MHF Hall of Fame
Dec 2007
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Zeitgeist
Jerome parks downtown in front of the barber shop. The meter is expired and takes only quarters. Jerome looks in the barber shop to see how many customers are waiting. He understands that if the meter man comes along and notices his car parked by an expired meter, he will receive a ticket that will cost $10. He thinks for a moment and decides not to insert a quarter in the meter. What does this tell us about his estimate of the probability that a meter man will come by while he is in the barber shop? Your answer must complete the following sentence and you must justify your answer.

The probability of the meter man coming by is (more or less) than (a fraction inserted here).


I know this has to do with mathematical expectation and I know how to compute ME from all of my other hw questions, but I do not know where to start on this one...can somebody please help me out!
Let p be the probability that the meter man comes. If he does not put a quarter in then the expected amount of money saved is (1 - p)0.25 - 10p ....
 
Mar 2010
110
0
so at most he is saving a quarter, and if the meterman comes he is out 10 bucks; he doesn't put the quarter in so he must think the probability of the meter man coming is slim to none. but is there a number i should be looking to solve for?

the probability of the meterman coming is more/less than a fraction is what i am supposed to answer.

does .25 - 10.25p = 0 ?????
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
so at most he is saving a quarter, and if the meterman comes he is out 10 bucks; he doesn't put the quarter in so he must think the probability of the meter man coming is slim to none. but is there a number i should be looking to solve for?

the probability of the meterman coming is more/less than a fraction is what i am supposed to answer.

does .25 - 10.25p = 0 ?????
I was hoping you would realise that you had to solve an inequality (surely the question was suggestive of that!): (1 - p)0.25 - 10p > 0.
 
Oct 2008
21
0
I'm a little confused about this question now. I did it another way and got a different answer

p = Probability Man Comes
1 - p = Probability Man Doesn't Come

Assume man does not pay the 0.25.

Then his expected payment is:

Nothing if the man doesn't come
10 if the man does come

i.e.

0(1-p) + 10p = 10p

He requires then that

10p < 0.25

i.e. his expected payment is less than 0.25 cent, or otherwise he would have paid the 0.25

therefore p < 0.025.

Is this answer incorrect??

@mrfantastic

In your method you use expected saving and you say:

He saves 0.25 if he doesn't get caught
He saves -10 if he does get caught.

Should it not be:
He saves 0.25 if he doesn't get caught
He saves -9.75 if he does get caught (-9.75 = -10 + 0.25) - Because he still saves the orignal 0.25 even though he gets caught?