probability; compound event, permutations
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Yesterday we determined that the probability of an event is given by:
P(E) = n(E)n(S)
Given a single event, e.g. P(choosing a club from a set of cards),the calculation is very straightforward.
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) =
Jacks Hearts
JH
SpadesDiamonds
P( Diamond or Spade) =
In the previous examples the compound event wasone 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?
one event or the other
P( Compound Event )
both events
P( A or B ) = P(A) + P(B) - P(A ∩ B)
Key idea: Mutually Exclusive
Jacks Hearts
JH
SpadesDiamonds
or not
P( A and B ) = P(A) P(B | A) .
** P(B | A) : probability of B, given that A has already occured
Key idea: Independent (flipping coins)
or not (drawing a pair of aces)
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?
Kopps always has 2 flavors of the day, so if she adds another scoop (burgandy cherry)how many cone arrangements are there now?
Ok, I need more flavors to choose from.
http://baskinrobbins.com/images3.5/spotlight/Irvspot_we_sell_fun.png
If Baskin Robbins has 31 flavors, how many 3 scoop cones can I create?
4 scoop cones?
n scoop cones?
Any ordered sequence of k objects taken from a set of n distinct objects is called a permutation.
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?