The document discusses probability calculations for compound events involving drawing cards or objects with multiple outcomes. It explains that the probability of drawing 2 hearts from a deck of cards is calculated as the probability of the first heart multiplied by the probability of the second heart given the first was drawn. The document also discusses permutations and combinations when arranging multiple objects or flavors from a set number of options.

1. Yesterday we determined that the probability of an event is given by:
n(E)
P(E) = n(S)
Given a single event, e.g. P(choosing a club from a set of cards),
the calculation is very straightforward.

2. Given a compound event (2 or more events occuring) the plot thickens.
What is the probability of drawing a Jack or a Heart out of a deck of playing cards?
P(Jack or Heart) =

3. Jacks Hearts
JH

4. P( Diamond or Spade) =
Diamonds Spades

5. In the previous examples the compound event was
one or the other. Jack or Heart, Spade or Diamond.
In other compound events, both events could occur.
What is the proability of picking 2 hearts out of a deck of playing cards?

7. P( Compound Event )
both events one event or the other
.
P( A and B ) = P(A) P(B | A) P( A or B ) = P(A) + P(B) - P(A ∩ B)
Diamonds Spades
Key idea: Independent (flipping coins) Key idea: Mutually Exclusive
or not (drawing a pair of aces) Hearts
Jacks
or not JH
** P(B | A) : probability of B, given
that A has already occured

8. When I have my tonsils out (soon) I am looking forward to the ice­cream.
I'm thinking, maybe a 3 scoop bowl would be a good place to start ­
probably vanilla, caramel cashew, and chocolate.
My wife is going to pick it up for me and will probably
get a cone (with the same flavors) for herself.
How many possible ways can her cone be arranged?

9. Kopps always has 2 flavors of the day, so if she adds another scoop (burgandy cherry)
how many cone arrangements are there now?

10. Ok, I need more flavors to choose from.
http://baskinrobbins.com/images3.5/spotlight/Irvspot_we_sell_fun.png

11. If Baskin Robbins has 31 flavors, how many 3 scoop cones can I create?
4 scoop cones?
n scoop cones?

12. Any ordered sequence of k objects taken from
a set of n distinct objects is called a permutation.

13. Permutations with restrictions:
The letters of the word INFARCTION are arranged at random.
How many permutations are there?
How many of the permutations have F as the third letter?
What is the probability that the last letter is a vowel?