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Dr. Math FAQ:
probability in the
Browse High School Probability
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Selected answers to common questions:
Odds vs. probability.
- Conditional Probability [07/18/1998]
What is the difference between drawing a blue marble conditional on
drawing a red marble, and drawing a red-blue combination of marbles?
- Drawing Marbles [02/01/1997]
A jar contains 2 red, 3 blue, and 4 green marbles. Niki draws one marble
from the jar, and then Tom draws a marble. What is the probability that
Niki will draw a green marble and Tom will draw a blue marble?
- An Explanation of Pascal's Triangle [2/27/1995]
My 10th grade daughter is having trouble finding a simple explanation of
Pascal's Triangle and its application.
- Fibonacci and Incoming Bits [09/08/99]
Given a transmitter sending 100 bits of random data over an ideal
communication channel, what is the probability that there will be three
consecutive 1's at least once in the sequence?
- Gambler's Fallacy [03/14/2003]
My co-worker prefers to bet the same set of five lottery numbers every time, but I say that the probability is the same if you randomly select any set five numbers for the same period of time. Who is right?
- Geodesics [12/15/1996]
Can you give me information on the math behind geodesics?
- Independent and Dependent Events [08/16/1998]
How do I find the probability of independent and dependent events? Can
you explain the difference?
- Line Segments and Size of Infinites [03/19/1997]
Divide a line segment into three parts, one half and one a quarter the
length of the line segment. Choose a point at random along this line
segment. What is that probability that this point lands in the 1/2
- Math Symbol for C [12/15/1997]
I am puzzled by one symbol of typing math. What does the upper case
letter C mean? As in (2C1) (3C1) / (47C2) = 6/1081.
- Montana Duck Hunters [11/27/2001]
Montana duck hunters are all perfect shots. Ten of them are in a duck
blind when 10 ducks fly over. All 10 pick a duck at random to shoot at,
and all 10 fire at the same time. How many ducks could be expected to
escape, on average, if this experiment were repeated a large number of
- Odds Slang for Probability? [02/06/1997]
Is "odds" slang for probability?
- Odds vs. Probability [12/06/1996]
What's the probability that a man can draw the numbers 2 and 7 from a hat
containing the numbers 1-8?
- One Person of Seven Born on Monday [8/30/1996]
If there is a 14 percent chance that any person selected at random was
born on Monday, what is the probability that, of any seven people
selected at random, exactly one was born on Monday?
- Poker Hand Odds [08/07/1997]
What are the odds of getting exactly one pair in five card stud poker,
using one 52-card deck?
- Powerball Lottery: Odds of Winning a Prize [09/02/2001]
How are the Powerball lottery odds established?
- Probabilidad de que Juan y María se encuentren [6/27/1996]
Juan y María quedan a encontrarse entre las 7:00 y 8:00 en un
- Probability and Genetics - Huntington's Disease [12/30/2001]
I am doing a math paper on Huntington's Disease. What does probability
have to do with genetics?
- Probability: Let's Make a Deal [4/29/1996]
Should the contestant stick with the original choice of doors or switch
and choose the other door? What about the lottery?
- Probability of Being Born on Monday [8/26/1996]
What is the probability that of any seven persons exactly one was born on
- Probability of Hitting Safely [11/06/2001]
Calculate the probability that a baseball player batting .357 would hit
safely in at least 56 straight games, during the course of a 162- game
regular season, assuming 4 at bats per game.
- Probability of Rolling a 6 on One Die [4/30/1995]
The following questions came up during a game of Risk...
- Probability of Two Dice Summing to 5 [09/22/2001]
If a person rolls two dice, what is the probability of getting a five as
- Probability of Two Male Children [7/5/1996]
If a family has two children, and the older child is a boy, there is a
50 percent chance the family will have two boys. However...
- A Truel [3/6/1995]
You and two of your friends get into a dispute and decide to solve it
with a "Truel", a three way duel.
- When to Add, When to Multiply? [10/30/2001]
When do you add and when do you multiply to compute probability?
- Why Add Probabilities in an OR Statement? [05/25/1999]
Why when we want to find the probability of, for example, rolling a 2 or 3 on a die, do we add the number of twos and threes?
- 2-Digit Number is Multiple of 14 [9/10/1996]
What is the probability that a randomly selected two-digit number is a
multiple of 14?
- 30 hat probability question [11/7/1994]
In a department store there are 30 cubbies of different hats. Each hat
has its own assigned cubbie box. However, there was an earthquake...
- 5 cards are dealt from a perfectly shuffled deck [03/16/1998]
If you are dealt the ace of spaces, what is the probability of being
dealt exactly 2 aces?
- An Absorbing States Problem [11/28/2000]
A mouse is in one of 4 rooms. If it finds cheese in the current room, it
stays there; if not, it exits to another room at random. What is the
probability it will get trapped? Are there any absorbing states?
- Advanced Probability as Used in a MAGIC [2/15/1995]
A MAGIC deck is composed of numerous subsets of cards that fall into
specific categories. A card can be in several categories, but that isn't
part of this problem. We would like to know how to calculate the
probability of having pulled a card from a subgroup in the deck by the
Xth turn, where X increases from 1 to whatever.
- Aircraft Disappearances [01/29/1998]
Seventy percent of the light aircraft that disappear while in flight in a
certain country are subsequently discovered...
- AND and OR in Probability [03/02/1998]
Picking slips of paper from a hat, and comparison of AND and OR in
- Are They Wearing Seatbelts? [3/26/1995]
80 percent of all California drivers wear seatbelts. If 4 drivers are
pulled over, what is the probability that all 4 will be wearing their
- Arranging Marbles in Boxes [09/16/1998]
Six marbles are placed in one of three different boxes. What is the
probability that each box contains two marbles?
- Assigning Committees using Probability [2/7/1996]
If a committee of 5 people is to be chosen from 12 couples with the
restriction that no husband and wife can be on the same committee, how
many possible committees are there?
- At Least One "6" in Three Dice Rolls, Summed Simply [04/20/2013]
A student who knows better still wonders why simply adding probabilities of individual
dice tosses does not correctly calculate the probability of rolling at least one "6" from three
rolls. Doctor Peterson points out the redundant counting of outcomes that this
method would entail, then shows three valid methods that do start with simple
- At the Box Office [03/08/1999]
A "random walk" probability problem.
- Average Time for a Mouse to Find Cheese [11/05/1997]
A mouse has three rooms to go into...
- Baccarat; a Casino Game [5/22/1996]
Information on the probabilities of baccarat.