MSTE

Question 1

Red Socks and Black Socks (Number of Socks)

Answer 1

4

Question 2

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

Answer 2

21

Question 3

Elmer’s Tennis Career

Answer 3

Champion- Father – Champion ( C-F-C)

Question 4

A Three Man Jury

Answer 4

Same Juries (One-man and Three Man Jury)

Question 5

Die be thrown until one gets a 6

Answer 5

6

Question 6

Common Carnival Game

Answer 6

9/256 or less than 1/28

Question 7

Chuck –a – Luck

Answer 7

8%

Question 8

Mr Brown

Answer 8

Gain of 2.79 Dollars per 36 Trials

Question 9

13 Spades

Answer 9

6.299 x 1012

Question 10

The game of Craps / America’s gambling game

Answer 10

0.49293

Question 11

An Urn Contains . . .

Answer 11

Subjective Answer (Just read)

Question 12

Two Strangers / choose one positive whole numbers

Answer 12

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

Question 13

Two Strangers / New York

Answer 13

Empire State Building

Question 14

Three Prisoners

Answer 14

Subjective Answer (Just Read)

Question 15

Cereal boxes

Answer 15

11.43 Box

Question 16

Eight Eligible Bachelors

Answer 16

7 𝟕/𝟏𝟓 or 7.47

Question 17

Tennis Tournament

Answer 17

4/7

Question 18

King Arthur

Answer 18

¼

Question 19

100 coins are tossed

Answer 19

0.07959

Question 20

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

Answer 20

0.664

Question 21

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

Answer 21

0.619

Question 22

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

Answer 22

0.597

Question 23

Three cornered Duel

Answer 23

Miss

Question 24

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

Answer 24

5/8

Question 25

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

Answer 25

21.5/36

Question 26

Election

Answer 26

8/10

Question 27

Player A and B / Pennies

Answer 27

(N/n) / (2)^N

Question 28

Marvin

Answer 28

Subjective Answer (Just Read)

Question 29

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

Answer 29

2/3

Question 30

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

Answer 30

0.866

Question 31

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

Answer 31

0.75

Question 32

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

Answer 32

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

Question 33

King’s Minter Boxes

Answer 33

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

Question 34

Airborne Spores / Gelatin Plates

Answer 34

1 / √𝟐𝝅𝒎 , 0.4/√𝒎

Question 35

A bread Salesman

Answer 35

0.568

Question 36

Two or more have the same birthday

Answer 36

23

Question 37

Same birthday / 50-50 chance

Answer 37

253

Question 38

Birthmate

Answer 38

𝐫(𝐫−𝟏)/𝟐

Question 39

Erewhon / Holidays / 365 day year

Answer 39

364

Question 40

Cliff

Answer 40

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

Question 41

Player M and Player N / Bankrupt

Answer 41

1/3

Question 42

Roulette

Answer 42

18/38 > 7.23/57.7 bet all at once

Question 43

Coin / landing on edge

Answer 43

0.354r

Question 44

9 inch glass rod / Blue Dot

Answer 44

3 inches

Question 45

52 playing cards / first ace

Answer 45

10.6th card

Question 46

Locomotives

Answer 46

119 71

Question 47

If a stick is Broken

Answer 47

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

Question 48

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

Answer 48

2, 5, 11

Question 49

Choose number of plays

Answer 49

10 Plays

Question 50

Shuffled Deck / average number of matches

Answer 50

1

Question 51

Typist / How many letters

Answer 51

1 0.368 ( probability of exactly r matches)

Question 52

Wise Man

Answer 52

Subjective Answer (Just Read)

Question 53

Unbiased Instrument

Answer 53

Subjective Answer (Just Read)

Question 54

Quadratic Equation

Answer 54

1 !

Question 55

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

Answer 55

1

Question 56

Two dimensional Walk

Answer 56

0.239

Question 57

Parallel Lines

Answer 57

Between 0 and 𝝅/𝟐

Question 58

Needle

Answer 58

𝟒/𝛑 𝟒𝐋/𝛑 (Arbitrary Length)

Question 59

Two Urns (Some Black Some White)

Answer 59

n < 2000