50 Challenging Problems in Probability (Summary)
KeyWords
Answer
Red Socks and Black Socks
4 (Number of Socks)
21 (If number of Black Socks is Even)
Elmer’s Tennis Career
A Three Man Jury
Die be thrown until one gets a 6
Common Carnival Game
Chuck –a – Luck
Mr Brown
13 Spades
The game of Craps / America’s gambling game
An Urn Contains . . .
Champion- Father – Champion ( C-F-C)
Same Juries (One-man and Three Man Jury)
6
9/256 or less than 1/28
8%
Gain of 2.79 Dollars per 36 Trials
6.299 x 1012
0.49293
Subjective Answer (Just read)
Two Strangers / choose one positive whole
numbers
1 (Natural Choice)
3 (Popular Choice)
7 (Popular Choice)
Two Strangers / New York
Three Prisoners
Cereal boxes
Eight Eligible Bachelors
Tennis Tournament
King Arthur
100 coins are tossed
Empire State Building
Subjective Answer (Just Read)
11.43 Box
7 7/15 or 4.47
4/7
¼
0.07959
Pepys wrote Newton
Three cornered Duel
Two Urns (101 red, 100 blacks)
Election
Player A and B / Pennies
Marvin
If a chord is selected at random
Duel in the town / 5 A.M , 6 A.M
King’s Minter Boxes
Engineereya’s Vlog
0.664 (At least 1 six when 6 dice are rolled)
0.619 (At least 2 sixes when 12 dice are rolled)
0.597 (At least 3 sixes when 18 dice are rolled)
Miss
5/8 (without replacement)
21.5/36 (with replacement)
8/10
(N/n) / (2)N
Subjective Answer (Just Read)
2/3 ( two points chosen at circumference)
0.866 (distance of the chord from the center)
0.75 (midpoint of the chord is evenly distributed)
23/144 (Best Answer)
1/6 (Approximated)
0.366 (100 to a box)
(1-1/n)n (100 replaced by n)
Airborne Spores / Gelatin Plates
A bread Salesman
Two or more have the same birthday
Same birthday / 50-50 chance
Birthmate
Erewhon / Holidays / 365 day year
Cliff
Player M and Player N / Bankrupt
Roulette
Coin / landing on edge
9 inch glass rod / Blue Dot
52 playing cards / first ace
Locomotives
If a stick is Broken
A bar is broken (Smallest, middle sized,
largest piece)
Choose number of plays
Shuffled Deck / average number of matches
Typist / How many letters
Wise Man
Unbiased Instrument
Quadratic Equation
Particle / 50-50 chance of moving 1 step north
or south
Two dimensional Walk
Parallel Lines
Needle
Two Urns (Some Black Some White)
Engineereya’s Vlog
𝟏𝟏/ √𝟐𝟐𝟐𝟐𝟐𝟐 , 𝟎𝟎. 𝟒𝟒/ √𝒎𝒎
0.568
23
253
𝐫𝐫(𝐫𝐫 − 𝟏𝟏)
𝟐𝟐
364
107//243 (Probability of disaster)
½ (Probability of Escaping)
1/3
18/38 > 7.23/57.7 bet all at once
0.354r
3 inches
10.6th card
119
71
¼ L (Average length of smaller piece)
0.386 (Calculus, average ratio)
2, 5, 11
10 Plays
1
1
0.368 ( probability of exactly r matches)
Subjective Answer (Just Read)
Subjective Answer (Just Read)
1!
1
0.239
Between 0 and 𝝅𝝅/𝟐𝟐
𝟒𝟒/𝛑𝛑
𝟒𝟒𝟒𝟒/𝛑𝛑 (Arbitrary Length)
n < 2000