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probability in the
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Selected answers to common questions:
Odds vs. probability.
- Probability of Independent Events [02/07/1997]
If the probability of an event is known, is there a formula that will
gives the probability of that event after a given number of trials?
- Probability of Infection [03/06/1998]
How many of six hermits can be expected, on average, to get a disease,
assuming the disease is transmitted until an infectious hermit visits an
immune hermit, and assuming one hermit visit per day?
- Probability of Making Triangle with Three Stick Pieces [02/24/2007]
Take a stick of unit length and break it into two pieces, choosing the
break point at random. Now break the longer of the two pieces at a
random point. What is the probability that the three pieces can be
used to form a triangle?
- Probability of Matching Envelopes and Letters [03/03/1998]
Using inclusion-exclusion to calculate probability of matching no, then
exactly one, letter with its envelope.
- Probability of Matching Times on a Clock [09/14/2004]
What is the probability of two different times within the same hour
ending in the same last digit, such as 8:13 and 8:43?
- Probability of Never Having a Losing Record [04/07/2001]
Suppose a football team plays 8 games, and the chance of winning any
particular game is 50%. What is the probability of completing the season
without more losses than wins?
- The Probability of Outcomes [2/20/1995]
In the sample space for a probability experiment, outcome A is twice as
likely as outcome B. Outcome C is two-thirds as likely as outcome B.
Outcome C is twice as likely as outcome D. Find the probability of each
outcome in the sample space.
- Probability of Picking Coins [01/12/2003]
Max has 5 coins in his pocket that total 47 cents. What is the
probability that he will reach into his pocket and pull out a dime,
and then without replacing it reach in and pull out a quarter?
- Probability of Picking in the Correct Order [4/12/1996]
Out of a population of 200 different amino acids, what is the probability
of selecting the correct 20 acids in the correct order on your first try.
- Probability of Rolling 2 At Least Twice [7/3/1996]
A fair die is rolled three times. Find the probability of rolling a "two"
at least twice.
- Probability of Success with Random Guessing [07/10/2008]
I read that if 25 students take a 10-question true or false test and
they all randomly guess at the answers, there is a 75% chance that at
least one of them will score 80% or better. How is that possible? It
seems too high to me.
- Probability of the Same Birthday within a Group [8/22/1995]
What is the probability that, in a room of 30 people, two people will
have the same birthday?
- Probability of Void Hand in Card Game of Bridge [12/02/2004]
What is the probability of being dealt a bridge hand void in a
specified suit from an ordinary deck of 52 playing cards?
- Probability of Winning a Solitaire Game [10/26/1995]
I am interested in finding out how to figure the probability of winning
the solitaire 'clock game'.
- Probability of Winning in Squash [06/23/1999]
In a game of squash tied at 8 all, determine whether the player receiving
the serve has a better chance of winning if she calls 9 or 10 points.
- Probability of Winning Roulette [5/16/1996]
How can we calculate, discuss, and demonstrate the probabilities and
mathematical expectations of roulette?
- Probability: Permutations and Combinations [12/10/2002]
How is probability related to permutations and combinations?
- Probability Philosophy and Applying Inference [10/11/2004]
If I flip a coin 4 times and they all turn out to be heads, what is
the probability that the coin is fair?
- Probability Problem in a Lewis Carroll Book [12/13/2008]
Say that 70 percent of a group of soldiers have lost an eye, 75
percent an ear, 80 percent an arm, and 85 percent a leg. What minimum
percentage must have lost all four?
- Probability Question from a Math Test [3/8/1996]
There are 15 homerooms in the school and 20 students in each homeroom. If
the principal selects 5 of the homerooms for a pizza party, what is the
probability of Mr. Smith's homeroom being selected?
- Probability that 6 Peas will Sink [1/23/1996]
We need to know the probability that all six of these durn peas will be
floating on top of the water before they are all six sunk down to the
bottom of the jug...
- Probability That a Function Has Real Roots [9/24/1995]
If r and s are numbers between 0 and 9, inclusive, what is the
probability, P, that the function f(x) = x2 +rx + s has real roots? This
question will consider only the case where r and s are integers.
- Probability that a Random Integer... [7/18/1996]
How do I figure out the the probability that an integer chosen randomly
would be an integer multiple of a given integer "n" ... or the
probability that it would be a multiple of 2...7, and so on...?
- Probability That a Sum Is Divisible by Three [11/04/2009]
How many ways can you choose three numbers from 1-100 whose sum is
divisible by three?
- Probability That Random Chord Exceeds Radius in a Circle [11/20/2004]
If a chord is selected at random on a fixed circle, what is the
probability that its length exceeds the radius of the circle?
- Probability That Someone Shares Your Birthday [05/14/2002]
How many people would you have to share a room with before the
probability that one of them shares your birthday is at least 50%?
- Probability Theory: Coincidental Birthday [06/21/1998]
In more than half the classes in a school, there are at least two
children with the same birth date...
- Probability Transition Matrices [02/10/1999]
How do you use probability transition matrices to find probabilities
after the first transition?
- Probability Tree Diagrams [8/22/1996]
What are the odds that two children will both be boys, firing once will
hit a target, cargoes will arrive ruined?
- Probability Trees [07/26/1998]
A bottle cap machine packs a defective cap in one box in ten. What is the
probability the next four boxes will have a defective bottle cap?
- Probability vs. Odds, Explained [03/21/2002]
Given a coin with heads on one side and tails on the other, what are the
odds in favor of getting heads, and the odds against?
- Probability with the Poisson Distribution [10/16/1998]
Can you help me find a probability using a Poisson distribution? I need
to be able to manipulate lambda.
- The Probable Pen in the Cereal Box [11/25/1999]
Six different-colored pens are offered as prizes in boxes of breakfast
cereal. How many boxes of cereal do you have to buy to get all six?
- Prove Sum nci = 2^n ... [05/30/1998]
I would like to know how to prove sum nci = 2^n with 0<=i<=n.
- Proving Conditional Probabilities [01/24/2001]
If P(B|A) is greater than P(B), prove that P(B^c|A) is less than P(B^c).
- Questions of Probability [03/22/1997]
Questions concerning probability, Venn diagrams, marbles, acorns, dice,
- Raffle Tickets [08/20/1997]
A man buys 5 tickets in a 100-ticket raffle. There are three prizes...
- Randbin [03/14/1999]
Consider an airplane that has 113 seats... what is the probability that
at most 113 will check in?
- Random and Pseudorandom Numbers [10/13/1998]
When are the numbers of a sequence truly random numbers and not
- Random Card Shuffling Probabilities [6/11/1996]
What is the probability of at least two eights being next to each other
in a random shuffling of a deck of cards. What about at least two cards
(2 eights or 2 queens etc.) being next to each other?