MATH 55(31) WD SMITH HOMEWORK #9 DUE TUES 29 APR AT CLASS START
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OK... we are all done with the syllabus.
So here are a selection of problems for review purposes.
I've ramped up the difficulty a bit to get you ready for the final...
These all will require some thinking and maybe trying a few approaches.


PROBLEM #0 (not worth any points :)
People seem divided on whether I should grade based on plan A or plan B
    my tests    midterm    final    homeworks   ExtraCred
A:    20         30         30         20         +
B:    25         25         25         25         +
tell me which plan A or B you prefer, or suggest your own weighting scheme
if you don't like A or B.  


PROBLEM #1:
Exponential decay of some radioisotope cauases it, after 100 years to be 90% gone
(only 10% remains).  What is the half-life of the isotope?


PROBLEM #2:
If you pick 3 cards from a deck, what is the ODDS that
the cards will be (ignoring their suits) Ace, 2, and 3,
not necessarily in that order?


PROBLEM #3: 
Suppose your expected remaining life is 60 years,
and you are 100% confident you will not live for 130 more years.
I claim from those 2 facts alone, you can deduce that
the probability you will still be alive in 20 years, is at
least 36.36%. Figure out why that is true and explain your reasoning.
Then deduce that the probability you will still be alive in 50
years, is at least X -- and please supply the biggest X you can
such that you know it is true?


PROBLEM #4: 
There are 5 urns of candy. They have inside them, respectively,
5%, 17%, 23%, 57%, and 91% blue candies.
You reach in blindly and pick one candy from
each urn. What is the expected number of blue candies that you will get?


PROBLEM #5:
You want to have $100,000 in 15 years.  So you deposit $X per month into
a savings account making 4% APR compounded monthly.  What should X be?


PROBLEM #6:
Here are some event-pairs. For each pair decide if the events are DISJOINT or OVERLAPPING,
and INDEPENDENT or DEPENDENT.

a) Pick an apple and find it has a worm.    It's moldy.
b) Get killed in a mugging tomorrow.        It rains tomorrow.
c) Roll a dice and get 6.                   No, get 5.
d) Picking random person, get a female.     It rains tomorrow.
e) Picking random person, get a female.     Get a boy <10 years old.


PROBLEM #7.
How many orderings of 10 people (half of them male)
will have 4 among the first 5 people being male?