Combining Events
P(Ac)
What is the probability of the complement of event A
P(A|B) represents what probability
Probability of Event A given Event B has occurred
How many possible outfits could Tim try on if he has
green and black pants
orange, tan, red, and green shirts
yellow, black and red sneakers.
2x4x3=24
The Venn Diagram was named after mathematician John Venn. In which century was John Venn born?
19th
Who won the superbowl?
9ers
Experiment: Roll two dice
Event A = Roll a 6
Event B = Sum of Dice is greater than 8
P(A and B)
What is 7/36
Event A: Draw a face card
Event B: Draw a Jack or King
What is P(B|A)?
8/12
36=729
Who is the best yahtzee player in the room?
Mr. McFarland
What is the rule stating that the more times an experiment is repeated the closer the relative probability gets to the probability of the outcome.
Event A: Roll a 4
Event B: Roll an odd #
What is P(A or B)?
4/6
P(A and B)=P(A)*P(B) if and only if
A and B are independent
A traveling nurse wants to visit as many countries as they can in their career. There are 195 countries in the world. The nurse will only be able to visit 45 of them. How many different groups of countries could they possibly visit?
195 combination 45 195!/(45!*(195-45)!=???? CALC!
What is Joseph R Curry Academic Center
What is #of outcomes that match the event divided by the # of total possible outcomes.
Experiment: Drawing 3 cards out of a deck of 52 (without replacement)
Event A: Drawing a 4 on Draw 1
Event B: Drawing a Queen on Draw 2
Event C: Drawing a face card on Draw 3.
P(A and B and C)=.0013273
The multiplication rule
P(A and B)=P(A|B)*P(B) or P(B|A)*P(A)
A salesman wants to visit 7 cities to sell their hair gel product. They are selecting from a list of 12 cities to travel to. What are all the possible routes this salesman could take?
12 permutation 7. 12!/(12-7)!=3,991,680
Cushing Academy lives by the motto (latin)
"virtute et numine" by valour and divine aid
All different methods of assigning probability.
What are subjective, relative, and classical.
Construct a Venn Diagram (one circle for Event A and one for Event B). This represents the sample space of the experiment. Highlight the area that represents the union of the two events, then highlight the area that represents the Combination of the two events.
Experiment: Selecting 5 marbles from a bag with 4 red marbles, 7 green marbles, 2 white marbles, and 1 black marble (without replacement)
P(R and B and W and G and W)
In that order.
.0002
Provide the equation for permutation and combination. How is the equation different? Explain why this slight difference is there.
See board. The equation is different, because with combination we divide by an additional factorial of the # of items selected in each group. This represents the different orderings of each group and eliminates each repeat. Leaving us with one outcome for each combination.
What are the odds of rolling a large straight on the first roll of 4 dice in yahtzee?
72/1296
The two requirements of a probability model.
What are
1. Probabilities sum to 1
2. Probabilities between 0 and 1 (inclusive)