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The probability of drawing another gold coin from the same box is 0 in (a), and 1 in (b) and (c). Thus, the overall probability of drawing a gold coin in the second draw is 0 / 3 + 1 / 3 + 1 / 3 = 2 / 3 . The problem can be reframed by describing the boxes as each having one drawer on each of two sides. Each ...
Two urns containing white and red balls. In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the ...
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
There are 5 pink marbles, 2 blue marbles, and 8 purple marbles. What are the odds in favor of picking a blue marble? Answer: The odds in favour of a blue marble are 2:13. One can equivalently say that the odds are 13:2 against. There are 2 out of 15 chances in favour of blue, 13 out of 15 against blue.
Pages in category "Probability theory paradoxes" The following 21 pages are in this category, out of 21 total. This list may not reflect recent changes. 0–9.
In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. [1] The formula is still used, particularly to estimate underlying probabilities when there are few observations or events that have not been observed to occur at all in (finite) sample data.
The probability of drawing a red and a club in two drawings without replacement is then 26/52 × 13/51 × 2 = 676/2652, or 13/51. With replacement, the probability would be 26/52 × 13/52 × 2 = 676/2704, or 13/52. In probability theory, the word or allows for the possibility of both events happening
Suppose now that the coin may be biased, so that it comes up heads with probability p. If p is equal to 1/2, the gambler on average neither wins nor loses money, and the gambler's fortune over time is a martingale. If p is less than 1/2, the gambler loses money on average, and the gambler's fortune over time is a supermartingale.