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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.

17,291 Questions
Math and Arithmetic
Statistics
Probability

What is the probability of obtaining exactly 4 heads in 6 flips of a fair coin?

The probability of a head in one flip is 1/2.

The probability of HHHHTT is (1/2)6 = 1/64

The possible correct flips are HHHHTT, HHHTHT, HHTHHT, HTHHHT, THHHHT, HHHTTH, HHTHTH, HTHHTH, THHHTH, HHTTHH, HTHTHH, THHTHH, HTTHHH, THTHHH, TTHHHH, each with a probability of 1/64.

Total probability is 15/64.

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Math and Arithmetic
Statistics
Probability

What event has a probability of 0?

-- The freezing over of Hell.

-- A confirmed sighting of flying pigs.

etc.

Besides anything that is impossible, as noted above, the simultaneous occurrence of two mutually exclusive events has a probability of zero: It is raining and it is not raining, it is on and it is off, etc.

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Math and Arithmetic
Probability

Is it unusual to get a 12 when a pair of dice is rolled?

no it is not unusual to get a 12 as it is impossible to know what you will get as. it is based on a number of factors like the size of die or speed of throwing etc. so it is not unusual to get a 12

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Math and Arithmetic
Statistics
Probability

What is the value of z if the area between -z and z is 0.754?

Since the normal distribution is symmetric, the area between -z and 0 must be the same as the area between 0 and z. Using this fact, you can simplify this problem to finding a z such that the area between 0 and z is .754/2=.377. If you look this value up in a z-table or use the invNorm on a calculator, you will find that the required value of z will be 1.16. Therefore, the area between -1.16 and 1.16 must be approximately .754.

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Probability
Job Training and Career Qualifications

How many non diamond face card?

There are 9 non-diamond face cards in a standard 52 card deck.

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Algebra
Probability

How many distinguishable permutations of letters are possible in the word critics?

The word critics has 7 letters which can be arranged in 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 ways. To see this, imagine placing one of the 7 letters in the first slot. Then place a different letter in the second slot (there are only 6 letters left now), then 5 and so on down to 1. We multiply because we must do each of these steps to create a rearrangement of the word critics.

The problem then is that critics contains 2 'c's and 2 'i's, which are indistinguishable. For example, we might count "rtiicsc" several times by switching the places of the 'i's or the 'c's even though we cannot tell the difference in the word. So, we must divide out the repetition, by dividing by 2! = 2 * 1 twice. This corrects the over-counting from the duplicate letters.

So the correct result is 7!/(2! * 2!) = 1260 distinguishable permutations.

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Math and Arithmetic
Statistics
Probability

What is the probability of rolling double sixes with 2 rolls of the die?

Rollin for dubs- check em

1/6 chance for rolling the first six. 1/6 chance for rolling the second one (independantly). when doing compound probability problems like this you multiply the chances of each soooo

1/6 x 1/6 = 1/36 chance of rolling dubs sixes (or any other number for that matter)

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Probability
Multiple Births

What are the odds of having albino twins?

About 1 in 5 million

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Statistics
Probability

What probability draw 2 cards sum is 9?

Assuming a standard deck of 52 cards with aces counting as 1 and all face cards counting as 10, there are:

16 ways of drawing an ace and an 8,

16 ways of drawing a 2 and a 7

16 ways of drawing a 3 and a 6

16 ways of drawing a 4 and a 5, for a total of 64 ways to draw 2 cards whose sum is 9.

There are 52!/(50!2!) = 1,326 ways to draw two cards, so the probability is 64/1326 = 0.048, or about 1 in 21.

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Earth Sciences
Probability

How was Caloris Basin created?

Probably by a big explosion caused by a meteor or a comet

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Statistics
Probability

A probability distribution is an equation that?

Associates a particulare probability of occurrence with each outcome in the sample space.

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Probability

How often does a bicentennial occur?

Every 200 years.

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Math and Arithmetic
Statistics
Probability

What is the sample space if you roll 2 dice?

The sample space for 2 dice is 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

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Statistics
Probability

How many red face cards are there in a set of playing cards?

The same number as there are black face cards. The face cards are King, Queen and Jack (they have faces). There are two red suits - hearts and diamonds. Therefore, two red Kings, two red Queens and two red Jacks. Six red face cards altogether.

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Definitions
Synonyms and Antonyms
Probability

What does fanciful mean?

1. characterized by or showing fancy; capricious or whimsical in appearance: a fanciful design of butterflies and flowers.

2. suggested by fancy; imaginary; unreal: fanciful lands of romance.

3. led by fancy rather than by reason and experience; whimsical: a fanciful mind.

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Math and Arithmetic
Statistics
Probability

What is the probability of flipping a coin and getting 1 head and 1 tail in any order?

50% chance: Here are the four possibilities: H.H, H.T, T.H, T.T; where the first letter is the first flip, and the second letter is the next flip (H means heads and T means tails).

So out of the 4 possible outcomes, 2 of them result in one heads and one tails. 2/4 = 50%.

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Probability

If a multiple-choice question has five answer choices and you submit one wrong answer before getting the question correct how much credit will you lose for that part of the question?

question with options, you will lose of the credit for that question. Just like the similar multiple-choice penalty on most standardized tests, this rule is necessary to prevent random guessing.

With five choices, your chance of getting the question wrong is 80% when guessing, and every wrong answer costs you 1/4 of a point. In this case, leave it blank with no penalty. Guessing becomes a much better gamble if you can eliminate even one obviously incorrect response. If you can narrow the choices down to three possibilities by eliminating obvious wrong answers

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Math and Arithmetic
Algebra
Probability

How many ways can you rearrange the letters in tattoo?

We can rearrange the letters in tattoo 60 times.

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Proofs
Statistics
Probability

A fair coin is continually flipped What is the probability that the first four flips are a. H-H-H-H b. T-H-H-H c. what is the probability that the pattern T-H-H-H occurs before the pattern.?

a) 1/16

b) 1/16

c) 1/256 [this answer was given, but it is unclear what part-c is even asking: The pattern occurs before what pattern? There are many variables which are unspecified and would affect the outcome.]

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Probability

When did they discover probability?

A gambler's 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 with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing 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 on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite. This problem and others 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, a teacher of Leibniz, learned of this correspondence and shortly thereafter (in 1657) published the first book on probability; entitled De Ratiociniis in Ludo Aleae, it was a treatise on problems associated with gambling. Because of the inherent appeal of games of chance, probability theory soon became popular, and the subject developed rapidly during the 18th century. The major contributors during this period were Jakob Bernoulli (1654-1705) and Abraham de Moivre (1667-1754). In 1812 Pierre de Laplace (1749-1827) introduced a host of new ideas and mathematical techniques in his book, Théorie Analytique des Probabilités. Before Laplace, probability theory was solely 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 l9th 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 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 Kolmogorov. that is the history!!!!!!

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Statistics
Probability

About the history of gamma distribution?

According to the links, Karl Pearson was first to formally introduce the gamma distribution. However, the symbol gamma for the gamma function, as a part of calculus, originated far earlier, by Legrenge (1752 to 1853). The beta and gamma functions are related. Please review the related links, particularly the second one from Wikipedia.

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Probability

Statistics and probability 7th grade?

yea a little in grade 7 you will likely go over that again in grade 8.

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Probability

What is union probability?

A union probability is denoted by P(X or Y), where X and Y are two events. P(X or Y) is the probability that X will occur or that Y will occur or that both X and Y will occur. The probability of a person wearing glasses or having blond hair is an example of union probability. All people wearing glasses are included in the union, along with all blondes and all blond people who wear glasses.

According to Professor Franz Kurfess of California Polytechnic State University, San Luis Obispo, union probability of two independent events A and B can be denoted as:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= P(A) + P(B) - P(A) * P (B)

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Science
Statistics
Birthdays
Probability

How many people share your birthday?

On average every day there are 1.9 million people celebrating their birthday. That is the total global population (7 billion) divided by the number of days in a year (365).

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