Also you might want to calculate the probability that LESS than half are chosen, since
P(0,1,2) are all zero. So you only need to calculate three values instead of 7.
Try thinking about the whole population of bottles.
X% are not defective.
Y% are defective.
Now you pick a bottle at random and drop it four times.
What can happen?
It could be defective and survive. (a%)
It could be not-defective and survive (b%)
It could be defective and break...
Here is a thin sketch of a proof. Then you can fill in the details and ask for help on steps you don't know how to do.
1) Take a Cauchy sequence c_n in l2. Construct a new sequence X by treating each coordinate as a Cauchy sequence in R (or C).
2) Show that X is in l2.
3) Show that c_n...
Well let's see. Someone has the gene 93% of the time, and when they do it's reported that they have it 99.9% of the time. So out of 100k people, 930 would have the gene but the test would say no.
7% of people don't have the gene, and it's reported that they do 10.3% of the time. So out of...
Categorize all the people into the following:
Has the gene/test says yes
Has the gene/test says no
No gene/test says yes
No gene/test says no
Figure out how many in each group. Then you should be home free to answer any questions about this test and population.
Well, you might want to look into Bayes' Theorem (try Wikipedia).
An intuitive way to do it is to create a large population, and then figure out what happens to it.
So suppose there are 100,000 people. How many of them actually have the disease? Suppose we test them all. How many are...
Hint: If you have a partition P_n, then each piece of a partition that contains a point where f is nonzero has an area of \frac{1}{n}. What you need to show is that for any \epsilon, there is an n such that no more than n\epsilon of the pieces contain a point where f is nonzero.
Try to do...
No, the question is asking for the chance that after 200 bombs were dropped, a particular block had not been hit.
You are right that P(not getting hit by a single bomb) = 99/100. So what's P(not getting hit by any of 200 bombs)?