Probab Looks Fam

Question 1

Red Socks and Black Socks

Answer 1

4 (Number of Socks)
21 (If number of Black Socks is even)

Question 2

Elmer’s Tennis Career

Answer 2

Champion-Father-Champion (0.512)

Question 3

A Three Man JUry

Answer 3

Same Juries ( One Man and Three Man jury)

Question 4

Die be thrown until one gets a 6

Answer 4

6

Question 5

Common Carnival Game, a player tosses a penny

Answer 5

9/256 or less than 1/28

Question 6

Chuck-a-Luck

Answer 6

8%

Question 7

Mr. Brown

Answer 7

Gain of 2.79 Dollars per 36 trials

Question 8

13 spades at bridge

Answer 8

6.299 x 10^12

Question 9

Game of Craps / America’s Gambling gme

Answer 9

0.49293

Question 10

Two Strangers / Choose one positive number

Answer 10

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

Question 11

Two Strangers / New York

Answer 11

Empire State Building

Question 12

Will Second-Best Be Runner-Up?

Answer 12

in a tournament of 2n players, the second-best man has probability 2^(n - 1) / (2^n - 1) of winning the runner-up cup.

Question 13

Coupons in Cereal Boxes

Answer 13

11.43 box

Question 14

Eight Eligible Bachelors

Answer 14

7 7/15

Question 15

Tennis Tournament

Answer 15

4/7

Question 16

King Arthur

Answer 16

1/4

Question 17

100 coins are tossed

Answer 17

0.07959

Question 18

Pepys wrote Newton

Answer 18

0.664 (At least 1 six when 6 dice are rolled)
0.619 (At least 2 six when 12 dice are rolled)
0.597 (At least 3 six when 18 dice are rolled)

Question 19

Three Cornered Duel

Answer 19

Miss

Question 20

Two Urns (101 red, 100 blacks)

Answer 20

5.8 (w/o replacement)
21.5/36 (with replacement)

Question 21

In an election, two candidates, Albert and Benjamin, have in a ballot box a
and b votes respectively

Answer 21

8/10

Question 22

Player A and B / Pennies

Answer 22

(N / n) / 2^N

Question 23

If a chord is selected at random on a fixed circle

Answer 23

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)

Question 24

DUel in the town / 5 AM, 6 AM

Answer 24

23/144 (Best Answer)
1/6 approximated

Question 25

King's Minter Boxes

Answer 25

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

Question 26

Airborne Spores

Answer 26

1/ sqrt of (2 pi m) , 0.4 / sqrt m

Question 27

A bread salesman sells on the average 20 cakes on a round of his route

Answer 27

0.568

Question 28

What is the least number of persons required if the probability exceeds! that two or more of them have the same birthday?

Answer 28

23

Question 29

You want to find someone whose birthday matches yours. What is the least number of strangers whose birthdays you need to ask about to have a 5O-5O chance?

Answer 29

365 293

Question 30

Labor laws in Erewhon require factory owners to give every worker a holiday whenever one of them has a birthday and to hire without discrimination on grounds of birthdays.

Answer 30

364

Question 31

Cliff

Answer 31

107 / 243 (Disaster) 1/2 (Escaping)

Question 32

Player M and N / Banktrupt

Answer 32

1/3

Question 33

Roulette

Answer 33

18/38 > 7.23/57.7 bet all at once

Question 34

How thick should a coin be to have a 1/3 chance of landing on edge?

Answer 34

0.354 pi

Question 35

Clumsy Chemist ( 9 Inch Glass Rod, Blue Dot)

Answer 35

3 inches

Question 36

52 Playing Cards / First Ace

Answer 36

10.6th card

Question 37

Locomotives

Answer 37

119 71

Question 38

If a stick is broken

Answer 38

1/4 L (Average length of Smaller Piece) 0.386 (Calculus, Average Ratio)

Question 39

A bar is broken (Small, Middle-Sized, Largest Piece)

Answer 39

2 5 11

Question 40

You get to choose in advance the number of plays. How many do you choose?

Answer 40

10

Question 41

Shuffled Deck / Average Number of Matches

Answer 41

1

Question 42

Typist / How many letters

Answer 42

1 0.368 ( probability of exactly r matches)

Question 43

Quadratic Equation

Answer 43

1!

Question 44

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

Answer 44

1

Question 45

Two-Dimensional Walk

Answer 45

0.239

Question 46

Parallel Lines

Answer 46

Between 0 and pi/2

Question 47

Needle

Answer 47

4/pi 4L / pi (Arbitrary Length)

Question 48

Needle

Answer 48

4/pi 4L / pi (Arbitrary Length)

Question 49

Two Urns

Answer 49

n<2000