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15 Cards in this Set
- Front
- Back
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A\B (A take away B) |
equals A∩Bcomplement if A={1,2,3} and B= {1,3,5} then A\B = {2} |
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If you flip a coin 3x in a row there are... |
2^3=8 possibilities (n=2, r=3) |
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Order counts with out replacement |
r≤n , there are n ways to choose the first object, total number of ways is n!/(n-r)! |
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0! equals |
1 |
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13!/1! equals |
13 |
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Order does not count without replacement |
(n!/(n-r)!)(1/r!) if order does not count, (2,1) and (1,2) are the same (define n choose r) |
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n choose 0 equals |
1 |
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n choose n equals |
1 |
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n choose 1 equals |
n |
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n is |
6 for a die 2 for a coin |
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r is |
the number of times a coin is tossed/ die rolled etc. |
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Order counts with replacement |
n^r different ways total |
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Order does not count with replacement (rare) |
n=1, r≥1...1 way n=2, r≥1...r+1 ways r=1, n≥1...n ways r=2, n≥2...n+1 choose 2 |
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toss a fair die twice in a row. what the probability that the numbers which come up are in non-decreasing order? |
Denominator: 6^2=36 (size of sample space) Numerator: (replacement, order does not count) n+r-1 choose r n=6, r=2 so 6+2+1 choose 2= 7 choose 2= 7x6/2x1= 21 21/36 = 7/12 probability |
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Independent events |
A and B are indenpendent in the probability of P(A∩B) =P(A)P(B) |
