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It is a hard (and often open) problem to calculate the minimum number of tickets one needs to purchase to guarantee that at least one of these tickets matches at least 2 numbers. In the 5-from-90 lotto, the minimum number of tickets that can guarantee a ticket with at least 2 matches is 100. [3]
This process can be generalized to a group of n people, where p(n) is the probability of at least two of the n people sharing a birthday. It is easier to first calculate the probability p (n) that all n birthdays are different. According to the pigeonhole principle, p (n) is zero when n > 365. When n ≤ 365:
In the simplest case, if one allocates balls into bins (with =) sequentially one by one, and for each ball one chooses random bins at each step and then allocates the ball into the least loaded of the selected bins (ties broken arbitrarily), then with high probability the maximum load is: [8]
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
At least one of them is a boy. What is the probability that both children are boys? Gardner initially gave the answers 1 / 2 and 1 / 3 , respectively, but later acknowledged that the second question was ambiguous. [1] Its answer could be 1 / 2 , depending on the procedure by which the information "at least one of them is a ...
(i) yields for all a success probability of at least 1/e, (ii) is a minimax-optimal strategy for the selector who does not know , (iii) selects, if there is at least one applicant, none at all with probability exactly 1/e. The 1/e-law, proved in 1984 by F. Thomas Bruss, came as a surprise.
B. Twelve fair dice are tossed independently and at least two "6"s appear. C. Eighteen fair dice are tossed independently and at least three "6"s appear. [3] Pepys initially thought that outcome C had the highest probability, but Newton correctly concluded that outcome A actually has the highest probability.