Competition problem — Combinatorics

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Combinatorics Difficulty 2.8 Junior Find the answer

There is a cup of 2 liters of water containing a single bacterium. If a small cup is used to take out 0.1 liters of water from this cup, what is the probability that the small cup of water contains this bacterium?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Consider the location of the bacterium as a single trial, and let the event that the small cup contains this bacterium be denoted as $A$ .

The volume of the region constituting event $A$ is 0.1 liters, and the total volume of all possible outcomes is 2 liters. Therefore, the probability $P(A) = \frac{0.1}{2} = 0.05$ .

Thus, the probability that the small cup of water contains the bacterium is $\boxed{0.05}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.