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50-Challenging-Problems-in-Probability-Summary > MSTE > Flashcards

MSTE Flashcards

1
Q

Red Socks and Black Socks (Number of Socks)

A

4

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2
Q

Red Socks and Black Socks (If number of Black Socks is Even)

A

21

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3
Q

Elmer’s Tennis Career

A

Champion- Father – Champion ( C-F-C)

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4
Q

A Three Man Jury

A

Same Juries (One-man and Three Man Jury)

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5
Q

Die be thrown until one gets a 6

A

6

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6
Q

Common Carnival Game

A

9/256 or less than 1/28

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7
Q

Chuck –a – Luck

A

8%

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8
Q

Mr Brown

A

Gain of 2.79 Dollars per 36 Trials

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9
Q

13 Spades

A

6.299 x 1012

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10
Q

The game of Craps / America’s gambling game

A

0.49293

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11
Q

An Urn Contains . . .

A

Subjective Answer (Just read)

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12
Q

Two Strangers / choose one positive whole numbers

A

1 (Natural Choice)
3 (Popular Choice)
7 (Popular Choice)

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13
Q

Two Strangers / New York

A

Empire State Building

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14
Q

Three Prisoners

A

Subjective Answer (Just Read)

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15
Q

Cereal boxes

A

11.43 Box

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16
Q

Eight Eligible Bachelors

A

7 𝟕/𝟏𝟓 or 7.47

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17
Q

Tennis Tournament

A

4/7

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18
Q

King Arthur

A

¼

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19
Q

100 coins are tossed

A

0.07959

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20
Q

Pepys wrote Newton (At least 1 six when 6 dice are rolled)

A

0.664

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21
Q

Pepys wrote Newton (At least 2 sixes when 12 dice are rolled)

A

0.619

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22
Q

Pepys wrote Newton (At least 3 sixes when 18 dice are rolled)

A

0.597

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23
Q

Three cornered Duel

A

Miss

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24
Q

Two Urns (101 red, 100 blacks)(without replacement)

A

5/8

25
Q

Two Urns (101 red, 100 blacks)
5 (with replacement)

A

21.5/36

26
Q

Election

A

8/10

27
Q

Player A and B / Pennies

A

(N/n) / (2)^N

28
Q

Marvin

A

Subjective Answer (Just Read)

29
Q

If a chord is selected at random ( two points chosen at circumference)

A

2/3

30
Q

If a chord is selected at random (distance of the chord from the center)

A

0.866

31
Q

If a chord is selected at random (midpoint of the chord is evenly distributed)

A

0.75

32
Q

Duel in the town / 5 A.M , 6 A.M

A

23/144 (Best Answer)
1/6 (Approximated

33
Q

King’s Minter Boxes

A

0.366 (100 to a box)
(1- 𝟏𝒏 )n (100 replaced by n)

34
Q

Airborne Spores / Gelatin Plates

A

1 / √𝟐𝝅𝒎 , 0.4/√𝒎

35
Q

A bread Salesman

A

0.568

36
Q

Two or more have the same birthday

A

23

37
Q

Same birthday / 50-50 chance

A

253

38
Q

Birthmate

A

𝐫(𝐫−𝟏)/𝟐

39
Q

Erewhon / Holidays / 365 day year

A

364

40
Q

Cliff

A

107//243 (Probability of disaster)
½ (Probability of Escaping)

41
Q

Player M and Player N / Bankrupt

A

1/3

42
Q

Roulette

A

18/38 > 7.23/57.7 bet all at once

43
Q

Coin / landing on edge

A

0.354r

44
Q

9 inch glass rod / Blue Dot

A

3 inches

45
Q

52 playing cards / first ace

A

10.6th card

46
Q

Locomotives

A

119
71

47
Q

If a stick is Broken

A

¼ L (Average length of smaller piece)
0.386 (Calculus, average ratio)

48
Q

A bar is broken (Smallest, middle sized, largest piece)

A

2, 5, 11

49
Q

Choose number of plays

A

10 Plays

50
Q

Shuffled Deck / average number of matches

A

1

51
Q

Typist / How many letters

A

1
0.368 ( probability of exactly r matches)

52
Q

Wise Man

A

Subjective Answer (Just Read)

53
Q

Unbiased Instrument

A

Subjective Answer (Just Read)

54
Q

Quadratic Equation

A

1 !

55
Q

Particle / 50-50 chance of moving 1 step north or south

A

1

56
Q

Two dimensional Walk

A

0.239

57
Q

Parallel Lines

A

Between 0 and 𝝅/𝟐

58
Q

Needle

A

𝟒/𝛑
𝟒𝐋/𝛑 (Arbitrary Length)

59
Q

Two Urns (Some Black Some White)

A

n < 2000

50-Challenging-Problems-in-Probability-Summary (1 decks)

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