April 09, 2014
Precalc Warm Up # 2-3
1. There are 40 numbered balls in a bag (1-40). If you
select one, find the number of ways you can select
a.
b.
c.
d.
2.
an even number
a number less than 10
a square number
a prime number
the primes are 2,3,5,7,11,13,17,19,23,29,31,37 so there are 12
4
11 1
25
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Probability is easy. It is just the number of favorable
ways an event can occur divided by the number of
total ways it could occur. The hard part is the
counting of these ways.
You can list the ways (like the prime number example
on the warmups), you can make tree diagrams, or you
could use formulas to help with this counting ( nPr if
you want an arrangement and order is counted, or nCr
You sometimes need duct tape (if objects have to be
together) , or you may want distinguishable ways.
(think of the hippopotamus problem)
And remember, you sometimes need to consider
separate cases, in which case you get the answers to
those cases separately, and then add them together.
--->
if you want a selection and order isn't counted).
April 09, 2014
Try:
1. How many different car licenses can be made in a
state where you have 3 letters followed by 3 digits?
2. The digits 0 through 9 are written on slips of
paper and put in a bag. Three are drawn out and
placed in the order they were drawn. How many
different outcomes are there?
As you can see, it is very important to consider
REPLACEMENT! Both of these problems were
ARRANGEMENTS, but the first problem replaced
and second one was without replacement.
April 09, 2014
3. Let's say that you can name a program that you
wrote with one or two characters. The first
character must be a letter, and second character
could be either a letter or a digit. How many
different program names are there under these
rules?
4. A horse race has 5 entries. In how many
different orders can the horses finish?
5. In the above race, how many different ways can
they come in 1st, 2nd, and 3rd place?
6. How many ways could I have bought 2 horses from
those 5?
April 09, 2014
6. In how many distinguishable ways can x5yz3 be
written without using exponents?
7. A Poker hand consists of 5 cards dealt from a
deck of 52. To find out how many different hands
are possible, why couldn't you do the following?
52 · 51 · 50 · 49 · 48 = 311,875,200 ways
How do you do this problem correctly?
8. If there are 6 couples that go to a concert
together, how many different ways can they be
seated if the couples want to be together? (show it
with the duct tape method, and with another
method)
April 09, 2014
Whether you are using nPr or nCr you are NOT
REPLACING. If you ARE replacing, you cannot use
these formulas.
If the situation was that you are dealt a card, and
noting what it was, you replace it in the deck. Then
another is dealt to you, and again you note what it
was and replace it in the deck. After you are dealt
5 cards in this manner, the number of different
outcomes would be
52 · 52 · 52 · 52 · 52
= 525 = 380,204,032 ways
April 09, 2014
What's the
probability of getting
a royal flush
on a single 5 card
deal ???
What's the
probability of getting
4 of a kind on a single
5 card deal?
13
C1 ·
4
C4 ·
12
C1
4
C1
= 624
ways
out of
52
C5
total hands, so
1/4165 or .042%
April 09, 2014
2-3 p. 655 boxed, 3,7,23, 27,
30-33,36,37 skip 13 and 17
#
on 35, the jobs are the same job
There will be a quiz this Friday over
SL book: 14.1, 14.2, 14.3
PC book: 10.6