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# Probability - Melody

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This will be my probability thread

http://en.wikipedia.org/wiki/Poker_probability

1) Permutation Question

2) A selection problems

http://web2.0calc.com/questions/probability_29

3) Not very hard

4) What is the probabiliy that a rook (castle) and a bishop will threaten each other on a chess board ?

http://web2.0calc.com/questions/a-castle-and-a-bishop-are-placed-on-different-squares-of-a-chessboard-what-is-the-probability-that-one-piece-threatens-the-other

5) Poker

http://en.wikipedia.org/wiki/Poker_probability

6,7) kids in a circle

http://web2.0calc.com/questions/in-how-many-ways-can-4-boys-and-4-girls-sit-around-a-circle-table-if-all-the-boys-sit-together-rotations-of-the-same-arrangement-are-still#r1

http://web2.0calc.com/questions/in-how-many-ways-can-the-10-kids-in-my-class-be-seated-in-a-circle-if-john-and-sam-insist-on-being-seated-diametrically-opposite-each-other_1

8)   distinct paths from one corner of a square to the other.    :/

http://web2.0calc.com/questions/each-small-square-has-a-side-length-of-one-unit-how-many-distinct-paths-of-six-units-are-there-from-a-to-b

9)  B***s in boxes

http://web2.0calc.com/questions/how-many-ways-are-there-to-put-6-b***s-in-3-boxes-if-the-b***s-are-distinguishable-and-the-boxes-are-distinguishable#rr19

10) lollies and lunchboxes

11) Using poisson distribution.

http://web2.0calc.com/questions/in-average-there-is-one-defect-per-100-m-of-magnetic-tape-a-what-is-the-probability-that-150-m-of-tape-have-no-defect-b-given-that-the

12) counting chord cuts in a circle

http://web2.0calc.com/questions/x_1-x_2-ldots-x_9-are-nine-points-on-the-circumference-of-circle-o-line-segments-are-drawn-connecting-each-pair-of-points-what-is-th

13) Probability - coloured cards

http://web2.0calc.com/questions/probability-of-a-deck-of-red-and-blue-cards

14) counting steps in a grid -    :)

http://web2.0calc.com/questions/how-many-9-step-paths-are-there-from-nbsp-nbsp-to-nbsp-nbsp-which-pass-through-nbsp

15)   Car number plates with a twist problem

16)   Cars in a carpark

http://web2.0calc.com/questions/there-are-24-cars-in-the-parking-lot-outside-of-my-building-they-are-all-either-2-door-or-4-door-are-either-white-black-or-red-and-are

17)  b***s in a box

http://web2.0calc.com/questions/a-box-contains-4-white-b***s-and-5-red-b***s-i-draw-3-of-them-out-of-the-box-one-at-a-time-without-replacement-what-is-the-probability-t

18)  Cards

http://web2.0calc.com/questions/perhaps-the-most-common-error-in-ranking-poker-hands-involves-confusing-the-order-of-a-straight-and-a-flush-a-straight-is-5-cards-with-cons

19)  I am not sure what this is, some kind of probability.  :/

http://web2.0calc.com/questions/1-nbsp-kai-cuts-out-all-the-page-numbers-of-a-book-he-takes-each-number-and-cuts-the-numbers-into-separate-digits-single-digit-numbers-a

20)  Statistics  with zscore BUT Binomial Distribution.

http://web2.0calc.com/questions/according-to-benford-s-law-example-10-6-page-227-the-probability-that-the-first-digit-of-the-amount-of-a-randomly-chosen-invoice-is-a-1-o

21) How many ways can you pair an even number of people off.   And other scenarios too.

http://web2.0calc.com/questions/in-how-many-ways-can-8-people-be-seated-around-a-square-table-with-2-people-on-a-side-two-configurations-are-considered-equivalent-if-one

22) How many ways can N peripherals be attached to k computers if every peripheral must be attached to exactly one computer and and every computer must be attached to at least one periferal.

So ther must be at least as many computers as peripherals    $$k\ge N$$

I believe that this is the formula that Nauseated presented us with

$$\displaystyle \sum \limits_{i=0}^{{N-1}} *(-1)^i*\binom{N}{i}* (N-i)^k$$

http://web2.0calc.com/questions/this-is-question-from-assignment-book

23)  7 digit numbers with conditions

24)  Combinations - vertices of a octahedron

http://web2.0calc.com/questions/two-of-the-vertices-of-a-regular-octahedron-are-to-be-chosen-at-random-what-is-the-probability-that-they-will-be-the-endpoints-of-an-edge-o

25)  combination probabiliy - Not too difficult.

http://web2.0calc.com/questions/four-prime-numbers-are-randomly-selected-without-replacement-from-the-first-ten-prime-numbers-what-is-the-probability-that-the-sum-of-the-f

26)  Lotto Probability

http://web2.0calc.com/questions/1-nbsp-in-the-smallstate-lottery-three-white-b***s-are-drawn-at-random-from-twenty-b***s-numbered-1-through-20-and-a-blue-superball-is

27) Playing cards probabilities

28) b***s - middle high level

http://web2.0calc.com/questions/there-are-four-red-b***s-and-two-white-b***s-in-a-jar-one-ball-is-randomly-removed-and-replaced-with-a-ball-of-the-opposite-color-the-jar

29) coin flipping

I made an intereresting discovery here.:)

30)  cards

31) Number Theory - New to me. :/

http://web2.0calc.com/questions/a-point-is-on-a-number-line-but-it-is-limited-to-being-at-0-1-or-2-at-each-step-the-point-moves-1-unit-left-or-right-if-the-point-is-a

32) Expected values and probabilities

http://web2.0calc.com/questions/1-nbsp-two-numbers-x-and-y-are-randomly-chosen-from-the-interval-0-1-what-is-the-expected-value-of-x-y

33)  Areas inside a square - great logic from Chris

http://web2.0calc.com/questions/1-nbsp-point-p-is-chosen-inside-square-abcd-what-is-the-probability-that-triangle-abp-has-a-greater-area-than-triangle-cdp

34) nonogon probability

http://web2.0calc.com/questions/a-a-regular-nonagon-9-sided-polygon-is-inscribed-in-a-circle-as-shown-below-three-of-the-9-vertices-are-selected-at-random-and-the-tri

35) Expected values

http://web2.0calc.com/questions/consider-a-random-variable-x-such-that-p-x-1-p-x-1-frac12

36) Expected values

http://web2.0calc.com/questions/1-nbsp-suppose-we-have-a-bag-with-8-slips-of-paper-in-it-six-of-these-have-a-1-on-them-and-the-other-two-have-a-3-on-them-what-is-the-ex

37) Expected values

http://web2.0calc.com/questions/1-nbsp-two-numbers-x-and-y-are-randomly-chosen-from-the-interval-0-1-what-is-the-expected-value-of-x-y

38)  Treasue hunt:

http://web2.0calc.com/questions/a-pirate-is-searching-for-buried-treasure-on-6-islands-on-each-island-there-is-a-frac-1-4-chance-that-the-island-has-buried-treasure

http://web2.0calc.com/questions/page/1663

40)  Train probability

http://web2.0calc.com/questions/alex-needs-to-catch-a-train-the-train-arrives-randomly-some-time-between-1-00-and-2-00-waits-for-10-minutes-and-then-leaves-if-alex-also

41)  Probability on a number line     (26/4/15 Mellie)

http://web2.0calc.com/questions/two-numbers-between-0-and-1-on-a-number-line-are-to-be-chosen-at-random-what-is-the-probability-that-the-second-number-chosen-will-exce

42)  Another geometry special     (29/4/15  Mellie)

http://web2.0calc.com/questions/in-triangle-abc-ab-5-bc-4-and-ca-3-point-p-is-randomly-selected-inside-triangle-abc-what-is-the-probability-that-p

43 )  Expected value

44)  lights and colours

http://web2.0calc.com/questions/a-point-is-chosen-at-random-on-the-number-line-between-0-and-1-and-the-point-is-colored-green-then-another-point-is-chosen-at-random-on-t

45) Children and lollies and did I just discover a formula  :/

http://web2.0calc.com/questions/in-how-many-ways-can-we-distribute-13-pieces-of-identical-candy-to-5-kids-if-the-two-youngest-kids-are-twins-and-insist-on-receiving-an-equ

46)  How many ways can 15 Identical candybars be distributed to 5 different children

(15+5-1) C 15  ways    (I think)

http://web2.0calc.com/questions/1-nbsp-4-students-are-running-for-club-president-in-a-club-with-50-members-how-many-different-vote-counts-are-possible-if-all-50-members

Learning sites for these lollie questions

http://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

http://en.wikipedia.org/wiki/Multiset

47)  Another lollie question from Mellie

http://web2.0calc.com/questions/we-have-8-pieces-of-strawberry-candy-and-7-pieces-of-pineapple-candy-in-how-many-ways-can-we-distribute-this-candy-to-4-kids#rr2

48)  LEFT FACTORIAL

The subfactorial or left factorial, written, is the number of ways that n objects can be arranged where no object appears in its natural position (known as "derangements.")

http://web2.0calc.com/questions/what-does-the-meaan#r3

49) A and B alternate to roll a die.  What is the prob that A rolls a 6 first.       (15/5/15)

http://web2.0calc.com/questions/a-and-b-take-turns-rolling-a-die-a-starts-the-winner-is-the-first-one-that-rolls-a-6-what-is-the-probability-that-a-wins

50)  Minimum number of marbles needed    (from Mellie)       (15/5/15)

http://web2.0calc.com/questions/a-bag-contains-some-marbles-each-of-which-is-one-of-four-colors-red-white-blue-and-green-at-least-one-of-the-marbles-is-red-the-comp

51) Chance of 4 winning games in a row in basketball  (from Mellie)    (15/5/15)

52) Nickels and Pennies   (from Mellie)     (15/5/15)

http://web2.0calc.com/questions/i-have-a-bag-with-5-pennies-and-3-nickels-i-draw-coins-out-one-at-a-time-at-random-what-is-the-probability-that-i-haven-t-removed-all-3-ni

53) How many 20 digit numbers are even (from Mellie)   (15/5/15)

http://web2.0calc.com/questions/how-many-20-digit-numbers-are-such-that-the-sum-of-their-digits-is-even

54)  What is the chance of makinga cyclic quad ?    (from Mellie)   (15/5/15)  (page 1769)

http://web2.0calc.com/questions/six-points-on-a-circle-are-given-four-different-chords-joining-pairs-of-the-six-points-are-selected-at-random-what-is-the-probability-that

Repeating probablility problem

http://web2.0calc.com/questions/monty-hall-problem

Probability question.

http://web2.0calc.com/questions/a-grid-with-3-rows-and-52-columnsmins-tiled-with-78-identical-2x1-dominoes-how-many-ways-can-this-be-done-such-that-exactly-two-of-the-domi

Very tricky selections question.      (Alan and Bertie   4/3/15)

http://web2.0calc.com/questions/in-poker-a-5-card-hand-is-called-two-pair-if-there-are-two-cards-of-one-rank-two-cards-of-another-rank-and-a-fifth-card-of-a-third-rank

http://web2.0calc.com/questions/each-small-square-has-a-side-length-of-one-unit-how-many-distinct-paths-of-six-units-are-there-from-a-to-b

http://web2.0calc.com/questions/mack-the-bug-starts-at-0-0-at-noon-and-each-minute-moves-one-unit-right-or-one-unit-up-he-is-trying-to-get-to-the-point-5-7-howeve

Probability - new formula from Nauseated.

http://web2.0calc.com/questions/how-many-ways-are-there-to-distribute-12-unlabeled-b***s-into-9-labeled-boxes

http://web2.0calc.com/questions/how-many-ways-can-3-identical-b***s-go-into-9-unique-boxes

Probability - counting

Probability - counting

http://web2.0calc.com/questions/this-is-question-from-assignment-book

An alternative diagram method from Alan - This is really neat

http://web2.0calc.com/questions/i-think-this-is-a-mutually-exclusive-question

Feb 1, 2015