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Because almost all numbers are normal, almost all possible strings contain all possible finite substrings. Hence, the probability of the monkey typing a normal number is 1. The same principles apply regardless of the number of keys from which the monkey can choose; a 90-key keyboard can be seen as a generator of numbers written in base 90.
The probability of hitting the jackpot varies between the different lotteries. Popular US lotteries have odds ranging from the astronomical 1 in ~300 million in Mega Millions (a double-pick lottery) to the fairly good 1 in ~170 thousand in the Wisconsin Lottery Badger 5 (a pick-5, 31 number lottery). Wheeling systems are usually intended to ...
The Megaplier is drawn by the Texas Lottery (before the cross-sell expansion on January 31, 2010, it was the only lottery to offer Megaplier); it is drawn by a random number generator (RNG). The odds for each Megaplier possibility are not uniform. [32]
Bridge Odds for Practical Players. Master Bridge Series. London: Victor Gollancz Ltd in association with Peter Crawley. ISBN 0-575-02799-1. Reese, Terence; Trézel, Roger (1986). Master the Odds in Bridge. Master Bridge Series. London: Victor Gollancz Ltd in association with Peter Crawley. ISBN 0-575-02597-2
Where more than 1 powerball is drawn from a separate pool of balls to the main lottery (for example, in the EuroMillions game), the odds of the different possible powerball matching scores are calculated using the method shown in the "other scores" section above (in other words, the powerballs are like a mini-lottery in their own right), and ...
A possible sequence in Penney's game: heads, tails, heads Graphs of best responses for Penney's games of sequence lengths 3 and 4 – each sequence is dominated by the sequence pointing to it with the given probability (italics) or odds (normal text) [1]
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable.
E.g. £100 each-way fivefold accumulator with winners at Evens ( 1 ⁄ 4 odds a place), 11-8 ( 1 ⁄ 5 odds), 5-4 ( 1 ⁄ 4 odds), 1-2 (all up to win) and 3-1 ( 1 ⁄ 5 odds); total staked = £200 Note: 'All up to win' means there are insufficient participants in the event for place odds to be given (e.g. 4 or fewer runners in a horse race).