AP Statistics : How to use the multiplication rule
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Example Questions
Example Question #31 : Probability
Charlene has 7 blue chips, and Karen has 5 green ones. They decide to mix them up in a bag, then Karen will pick 5 chips and Charlene gets the rest.
What is the likelyhood Karen ends up with 5 chips of the same color?
There are 2 ways Karen gets 5 chips of the same color: she gets all 5 greens, or 5 blues. there is only 1 way to get all 5 greens: probability of which can be calculated as;
to calculate p(allblue) we use:
since order doesn't matter and chips are being drawn without replacement, this is an acceptable calculation and summing them yields
Example Question #32 : Probability
A ninja is training for his super secret mission, throwing grappling hooks at targets 
Total likelihood of making the shot = sum of likelihood of making 1st shot+2nd shot+...
1st shot=
2nd shot=.
3rd shot=
4th=
5th=
6th=
Example Question #33 : Probability
Frank of the forest is a monkey man who was raised by chimpanzees from a very young age. He enjoys swinging with his monkey friends. When Frank jumps from one tree to another, the chance that he falls increases by 10% for every foot he jumps past his armspan of 3 feet. (he has a 10% chance of falling at 4ft)
One day, Frank watches his monkey friends do 
Frank knows from experience not to take a jump route if the likelihood of him falling goes above 
Frank can finish this route, none of the jumps have above a 
After 
After 
After 
After 
After
This is multiplication rule. let's calculate the chance frank doesn't fall.
For the first jump this is 
Since the 7th jump drops his survival rate below 
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