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Unformatted text preview: (4.1) Basic Counting Rule Flipping a coin: BCR Tree Diagram Number of ways a class of 20 students can decide to come to class: *each student can decide yes or no, so 20 students have 2^20 ways of deciding to come to class* Rolling 4 6-sided Dice: *rolling 4 dice, each one has 6 options so you have 6^4 ways of rolling 4 dice* Finding Probabilities using BCR : Example: 3 people get into an elevator and choose to get off at one of the 10 remaining floors. Find the following probabilities: **total of 10^3 ways of getting off the elevator so denominator will be 10^3 for all** P(they all get off on different floors) = 10*9*8/10^3 P(they all get off on the 5 th floor) = 1/10^3 P(they all get off on the same floor) = 10*1/10^3 **10 different floors to choose from** P(exactly one of them gets off on the 5 th floor) = 3*9^2/10^3 **3 ways one can choose to get off on 5 th floor** P(at LEAST one of them gets off on the 5 th floor) = 1-P(no one gets off on 5 th floor) = 1- 9^3/10^3 Example: There are 4 different kinds of sandwiches: Ham, Turkey, Roast Beef, Veggie. You can have either Swiss, American or Provolone Cheese and have it on Rye, White or Wheat bread. Then you have the option of 12 additional condiments such as dressing, mayo, pickles, peppers, lettuce, tomatoes etc. How many different sandwiches can be made? **4*3*3*2^12** Example : With and Without Replacement: Snack pack of skittles contains 20 candies 5 are Red 15 are either O, G, Y, or P Select 3 candies WITH replacement Select 3 candies WITHOUT replacement P(all 3 red) P(exactly ONE red) P(at LEAST one red) Example: Bike Lock: (4 slots, numbers 0-9) If all combinations are equally likely find the following probabilities: P(combination contains only even numbers) P(combination starts and ends with an odd number) P(combination has no repeated values) P(combination has at least one 4) P(combination has either three 4s or three 5s)...
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- Spring '08