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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 6 rolls of a fair die will show exactly three fives?
The probability of getting three fives in the first three rolls and non-fives
in the
next three rolls is; P(5,5,5,N5,N5,N5) =
1/6 x 1/6 x 1/6 x 5/6 x 5/6 x 5/6
=
0.002679...
The number of different order in which the fives can come out is given by;
6C3 =
6!/[3!∙(6-3)!] =
20
So the probability that in 6 rolls of a fair die exactly three fives (in any order) will
come out is; P(three
fives any order) =
(20)∙(1/6)3∙(5/6)3 =
0.05358... ~ 5.4%
1/16
When a coin is tossed 7 times in a row what is the probability that heads comes up?
The chance is 3.5/7.
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 would be the probability that two straight haired parents would have a curly haired child?
1/4 100% however if one parents hair is even slightly wavy, the child could have curly hair
If you mean 43%, then the probability that it will not snow is 57%, 0.57 or 57/100.
What is the probability of a given number to be prime?
I don't think that there is one, as there are prime numbers for infinity, and they are not at an equal distance or at a distance which goes up at a certain rate, and so I'm pretty sure that there isn't one! I hope this answers your question!I don't think that there is one, as there are prime numbers for infinity, and they are not at an equal distance or at a distance which goes up at a certain rate, and so I'm pretty sure that there isn't one! I hope this answers your question!
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 does probability apply to genetics?
Probability is used in genetics to determine the possibilities of offspring having a particular trait
What is the probability of getting heads only once if a fair coin is tossed 3 times?
If heads comes up on the first throw (p=0.5) then tails must come up on the next two throws (each has a p= 0.5 of occurring) so 0.5 x 0.5 x 0.5 = 0.125 for this event (HTT) The second event is THT and the third event TTH each has a 0.125 probability, so 3 x 0.125 = 0.375. You can also solve this problem with the binomial distribution p = 0.5 q= 0.5, p(x=1, n= 3) = 3!/(2! 1!)(0.5)^1(0.5)^2 = 0.375 If heads comes up on the first throw (p=0.5) then tails must come up on the next two throws (each has a p= 0.5 of occurring) so 0.5 x 0.5 x 0.5 = 0.125 for this event (HTT) The second event is THT and the third event TTH each has a 0.125 probability, so 3 x 0.125 = 0.375. You can also solve this problem with the binomial distribution p = 0.5 q= 0.5, p(x=1, n= 3) = 3!/(2! 1!)(0.5)^1(0.5)^2 = 0.375
What is the probability that the total will be 8 when you roll two dices?
the answer is 5/36 coz (2,6) (3,5) (4,4) (5,3) (6,2) which are the five possible outcomes out of the 36 total no. of outcomes. Enjoy!! Kush
If two dice are rolled one time what is the probability of getting the number 8?
Sum of two dice eqauls 8:
2,6
3,5
4,4
5,3
6,2
= 5 in 36
How do you do probability in math?
The Probability of Success = Number of successful outcomes/Number of outcomes.
E.g. Find the probability of choosing a red five or a black odd numbered card in a standard deck of 52 playing cards.
There are 2 red fives and 10 odd numbered cards, and a total of 52 cards, so:
=2/52+10/52
=12/52
3/13
Probability of Red 5 or a Black Odd = 3/13
* * * * *
The above is true only for discrete distributions, not for continuous variables. For a continuous variable, with probability distribution function p(x), the probability that x lies between two values, a and b (ie a
What is the probability of drawing a king of hearts from a regular deck of 52 cards?
(question not clear) , as far to my understanding it is 4 over 52 simplified ,
so answer is = 1 over 13. (probability of a king drawn from a pack of cards)
How do you calculate expected value for a probability situation?
simulate 100 events where 12 students have been accepted and each student is 66% likely to accept. andministrators want to try to ubderstand how many students will attend the school
If there are 5 questions, each with 2 possible answers, there will be 25 different quiz outcomes possible. We know that 25 = 32 different possible outcomes on a competed quiz where one answer is selected for each question.
If DNA test says 0 probability can it be wrong?
Only if a mistake happened in the lab. This could be due to a mislabeled tube a sample placed in the wrong tube or any number of other misplaced samples or data. Most labs have systems in place to minimise these errors but none are perfect. Humans carry out these tests and humans make mistakes.
Rainfall of a day is cumulative rainfall recorded at fix time for past 24 hours. For example rainfall of 26th September at given place in India is amount of rainfall recorded between 3 GMT of 25-9-09 and 3 GMT of 26-09-09.
However rainfall can commence at any time of day say 5 GMT and continued for 5 GMT of next day. Thus rainfall record gets divided one between 5 GMT to 3 GMT and second 3 GMT of next day to 5 GMT conclusion of rain.
It is obvious that 24 hr rain ( 5 GMT to 5 GMT) is more than that of 1 day rain (either 5 GMT to 3 GMT of next day or 3 GMT of next day to 5 GMT conclusion of rains). One day rain is available with Ordinary raingauges (ORG) while 24 hr rain requires Self Recording Raingauges (SRRG). For Design Storm computations 24 hr rain has significance but data record is less than 1 day record.
As a compromize clock hour correction ( 24 hr rainfall / 1 day rainfall ) is worked out for available record where both ORG and SRRG observations are available. The average clock hour correction is then applied over 1 day PMP to get 24 hr PMP value.
N.Y.Apte
Hydrometeorologist
India meteorological Department
New Delhi
