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In the three-card problem, three cards are placed into a hat. One card is red on both sides, one is white on both sides, and one is white on one side and red on the other. If a card pulled from the hat is red on one side, the probability of the other side also being red is 2 / 3 . 53 students participated and were asked what the ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly at a constant rate of 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc.
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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 ...
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]
The problem is insolvable because any move changes by an even number. Since a move inverts two cups and each inversion changes W {\displaystyle W} by + 1 {\displaystyle +1} (if the cup was the right way up) or − 1 {\displaystyle -1} (otherwise), a move changes W {\displaystyle W} by the sum of two odd numbers, which is even, completing the proof.
The forward algorithm is one of the algorithms used to solve the decoding problem. Since the development of speech recognition [ 4 ] and pattern recognition and related fields like computational biology which use HMMs, the forward algorithm has gained popularity.