Question

Suppose a dot is placed at random in a 10x10 graph grid in which squares have been numbered from 1 to 100 with no number repeated. Now simulate 100 students choosing a number at random between 1 and 100 inclusive. How many students might you expect to choose the square with the dot?

Answer 1

Hum...

Answer 2

Help

Answer 3

I had to go back to the book for this one!

Answer 4

First I though of multiplication principle and independent event:
P(number) = 0.01
P(dot) = 100*0.01 = 1
But that doesn't give the expected number of times the dot is chosen.

Then I was thinking of this as follow:
A lot containing 100 components is sampled. The lot contains 99 good components and 1 defective component. A sample of 100 is taken (with replacement). Find the expected value of the number of bad components in the sample.

Answer 5

Ok another though, what about going with a Bernoulli trial.

Answer 6

Boy, if you get an answer to this, let me know. It's killing me!

Here's the Bernoulli trial idea:
Each student is a "trial". Each trial is independent.
success = picked dot.
P(success)=0.01
X = # of successes in 100 trials
probability distribution of X is b(x;100,0.01)
which when graphed: http://www.wolframalpha.com/input/?i=%28100+choose+x%29+*+%280.01%29^x+*%280.99%29^%28100-x%29plot+for+x+%3D+0+to+x%3D10
This seems to show that the greatest probability is with 0 or 1 success.
P(0 successes) is about 0.37
p(1 success) is about 0.37 as well
p(2 successes) is about 0.18, and drops sharply after that.

So based on the probabilities, it looks like you could expect maybe 1 or even none.