Fundamental Counting Principle
Multiplication Rule
Addition Rule
Permutations
Combinations
100
Simple or not Simple:
Choosing a CD
Simple Event
100
The probability of event B given A already occurred
P(A|B)
100
Mutually Exclusive or not
Event A: Drinking Monster
Event B: Red Bull
Mutually Exclusive Events
100
Permutation occurs when...
Order Matters!!!
100
Combination occurs when...
Order Doesn't Matter!!!
200
Double Down:
Draw a tree diagram
3 salad, 3 entrees, 3 desserts (in order)
200
The probability of selecting a 10, given selecting a Jack without replacement
4/51 or 7.84%
200
Double Down:
The Addition Rule for Not Mutually Exclusive Events
P(A U B) = P(A) + P(B) - P(B|A)
200
Double Down:
Permutation involving a duckling
Ways to pick a duckling from prettiest to ugliest
200
Permutation or Combination
Jerry has 10 dance moves, and can do 6 in one minute
Combination
300
The number of outcomes on a 5-digit combo (with no repeats)
300
The probability of rolling a 5, flipping heads, and on a four-color wheel spinning a purple
1/6*1/2*1/4=1/48 or 2.1%
300
The probability of selecting a Jack, Queen, or King as the first card
12/52 or 23.1%
300
10P10
3,628,800 outcomes
300
37C4
66,045 outcomes
400
Probability of not selecting a long hair student
8/23
9/21
400
Double Down:
The probability of selecting a Jack, then selecting another Jack without replacement
4/52*3/51=12/2652=1/221 or 5.43%
400
The probability of selecting a 4, 7, or spades as the first card
19/52 or 36.54%
400
The probability of getting a medal (gold, silver, bronze) out of 8 runners
(3 nPr 3)/(8 nPr 3) = 6/336=1.79%
400
The probability of winning the lottery from drawing five numbers out of 69 numbers
(5nCr5)/(69nCr5) = 1/11238513=0.000000089 or 0.0000089%
500
The probability of answering true on all 10 questions.
0.5^10 =.10%
500
The probability that someone will get a flush
154440/311875200 or 0.050%
500
Probability of not getting a face card as the first card
1-9/52 = 43/52 or 82.7%
500
The number of ways of going to a hot pot restaurant and choosing from 6 different broths, 4 types of meat, and 15 vegetable plates
Distinguishable Permutation
(25!)/((6!*4!*15!)) = 686,439,600 ways
500
Double Down:
The probability of being dealt five face cards from a standard deck of cards (scientific notation)
(9nCr5)/(52nCr5) = 4.85x10^-5 or .0050%