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Probability

The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.

14,643 Questions

What is the probability that if you roll the dice you'll get the number 100?

That depends on what kind of dice you are rolling and how many of them you roll. If you roll two 6-sided dice once, the probability of getting the number 100 is exactly zero. You cannot get a 100 on one roll of two 6-sided dice. Other dice and different numbers of them may yield different probabilities.

What are the chances of being shot as a cop?

The first answer wasn't valid at all.

The first answer 5 out of 3 doesn't make sense. It would depend a lot on where you were enforcing the law as well as what type of law enforcement you do. Someone in Tokyo would have almost no chance, while someone in Bahgdad would be almost certain to have a gunfight at soome point. In the US it is uncommon for the average policeman to ever fire his weapon in the line of duty, except at the range.

There are 6 numbers on a normal dice What is the probability that if you roll the dice you'll get the number 100?

Since the numbers (number of dots) on normal dice only go from 1 - 6, then I would think the probability of getting the number 100 is zero.

There are 36 different outcomes possible when you toss two dice. What is the probability that the two dice will show the same number?

There are 6 different doubles that can be rolled. (They are 1 and 1, 2 and 2, etc.) You have a 6/36 chance of rolling doubles. The fraction 6/36 simplifies (reduces) to 1/6. Your 1 in 6 chance of rolling doubles now needs to be converted to probability. Probability speaks to the "chance" that something will occur. It is expressed as a "pure" number, and the range of probability is from 0 to 1. The probability 0 means that it cannot occur, and the probability 1 means that it will or must occur. Everything else falls in between. If you have a 1 in 6 chance of rolling doubles that translates into a 1 divided by 6 probability, or a 0.1666666... probability that a double will come up.

What is the probability of getting the ace of spades?

Usually 1/52, Unless Jokers are included in whatever game, then it would be 1/54. This is of Course subjectively requiring that you have only one full deck of playing cards, and only one Ace of Spades

When did the study of probability begin?

A gamblers dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Méré, a French nobleman who was interested in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in tossing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well established gambling rule led de Méré to believe that betting a double six in 24 tosses would be profitable, but when he did his own calculations they indicated the opposite.

This and some other problems posed by de Méré led to an exchange of letters between Pascal and Fermat in which the fundamental principles of probability theory were formulated for the first time. Although a few special problems on games of chance had been solved by some Italian mathematicians in the 15th and 16th centuries, no general theory was developed before this famous correspondence.

The Dutch scientist Christian Huygens learned of this correspondence and in 1657 published the first book on probability: titled De Ratiociniis in Ludo Aleae, it was a treatise on problems associated with gambling. Because of the inherent appeal of games of chance, the theory soon became popular and the subject developed rapidly during the 18th century. The people who mainly contributed during this period were Jakob Bernoulli and Abraham de Moivre.

In 1812 Pierre de Laplace introduced a host of new ideas and mathematical techniques in his book, Théorie Analytique des Probabilités. Before Laplace, probability theory was only concerned with developing a mathematical analysis of games of chance. Laplace applied probabilistic ideas to many scientific and practical problems. The theory of errors, actuarial mathematics, and statistical mechanics are examples of some of the important applications of probability theory developed in the 19th century.

Like so many other branches of mathematics, the development of probability theory has been stimulated by the variety of its applications. Conversely, each advance in the theory has enlarged the scope of its influence. Mathematical statistics is one is one important branch of applied probability; other applications occur in such widely different fields as genetics, psychology, economics and engineering. Many workers have contributed to the theory since Laplace's time: among the most important are Chebyshev, Markov, von Mises and Kolomogorov.

One of the difficulties in developing a mathematical theory of probability has been to arrive at a definition of probability that is precise enough for use in mathematics, yet comprehensive enough to be applicable to a wide range of phenomena. The search for a widely acceptable definition took nearly three centuries and was marked by a lot of controversy. The matter was finally resolved in the 20th century by treating probability theory on an axiomatic basis. In 1933 a monograph by a Russian mathematician A. Kolmogorov outlined an axiomatic approach that forms the basis for the modern theory. Since the ideas have been refined somewhat and probability theory is now part of a more general discipline known as measure theory.

What are the chances of your son going into the NFL?

lets say you have a better chance of winning the lottery you have a better chance of getting hit by lightning then winning the lottery

If you draw a card from a normal deck of cards what is the probability the card is an jack of diamonds?

1/52 Which as a decimal is 0.01923076923076923076923076923 Which as a percent it is

1.923076923076923076923076923% (: Well, probably not exactly what you wanted but here some math. Oh and that number is real I did it on a calculator! Check it!

What is the probability of rolling a number less than 3 with one roll of a number cube?

There are two numbers less that three and 6 possible outcomes, so 2/3 or the time you would have a number less than three. So probability is 2/3 or 66% Alternate explanation: 2 to 1 against. A six sided die has two numbers less than three and four numbers three or more, so the odds of less than three are 2 in six, or 1 in three.

Three fair coins are tossed- whats the probability of tossing at least one head?

The chance for each toss is 1/2. The chance of all three flips being tails is 1/2 * 1/2 * 1/2 = 1/8. So the probability of at least one head is 7/8.

What is the probability of getting 2 heads in 2 coin tosses?

This can be calculated easily by multiplying the chances of getting one head in one toss for a fair coin (half) by itself(half) to give a quarter (1/4 or 1 in 4). If you wanted the chances of at least one head in 2 tosses, then the chances would be for anyhting exept 2 tails in a row, which is 1 - 0.25(quarter), which is 0.75 (3/4 or 3 quarters or 3 in 4)

How would you compare theoretical probability and experimental probability for getting three heads to the theoretical probability. would you expect the probabilities to be equal .?

I'm going to assume you're looking for the probability of getting three heads out of three coin spins and that you're using a fair coin. For coin spins, theoretical probability is very simple. The probability of getting three heads in a row is 1/2 * 1/2 * 1/2 = 1/8. This means that if you tossed a coin three times, you'd expect to see three heads once every 8 trials. For experimental probability you need to define clear trials, for this experiment you can't just spin a coin over and over and count the number of times you see three heads in a row, for example, if you threw the following: H T H H T T H H H H H T T H T T T you have three cases where you have three heads in a row, but they all overlap so these are not independent trials and cannot be compared to the theoretical result. When conducting your experiment, you know that if you get a T in your trial, it doesn't matter what comes after, that trial has already failed to get three heads in a row. The trial is deemed a success if you get three heads in a row, naturally. As a result, if you threw the above sequence, you would to determine your experimental probability in the following way: H T fail H H T fail T fail H H H success H H T fail T fail H T fail T fail T fail In this example we have 8 trials and one success, therefore the experimental probability is 1/8. The sample variance (look it up), however is also 1/8, meaning that all you really know is that the experimental probability could be anywhere between 0 and 1/4. The only way to get the variance down (and therefore reduce your confidence interval) is to perform more and more trials. It's unlikely for the theoretical probability and experimental probability to be EXACTLY the same but the more trials you do, the more the experimental probability will converge on the theoretical probability.

How do you play marbles?

Draw a circle. Everyone puts marbles in the circle and tries to shoot them out of the circle . When you shoot one out it becomes yours. A larger marble is used as the "shooter".

What is the probability of getting a black face card?

There are 6 black face card in a deck of 52 cards, so the probability of getting a black face card is 6/52 = 3/26

What diagonals are always perpendicular?

The diagonals of a square are always perpendicular.

If X is a normal random variable with standard deviation 4.00 and if the probability that X is more than 5.52 is 0.305 then what is the mean of X?

Denote by mu the mean of X. Given

P(X>5.52)=0.305

i.e.,

P((X-mu)/4> (5.52-mu)/4)=0.305

So, letting Z=(X-mu)/4. Then Z~N(0,1). Hence, the above equality is

P(Z>(5.52-mu)/4)=0.305. So,

(5.52-mu)/4=0.51

So,

mu=5.52-4*0.51=3.48

So, the best answer is 3.5

What does it mean when an escort saids she is a spinner?

"Spinner" (Adjective - Slang) Used among some men to describe an extremely petite young woman, usually with a lot of sex appeal - the term is thought to reference the small stature and weight of the woman; (IE she is so petite she could be spun around while riding the man during sex). Ex: Man #1- "Aw man, look at that girl, she's so tiny." Man #2- "yeah, she's a spinner."

What is the probability of a coin?

If you mean what is the probability of getting a heads/tails, it is a 1 in 2 chance (50/50 chance). You are just as likely to get a heads as you are to get a tails.

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