Probability

2000004703

Level: 
A
There is a wooden cube with faces painted in green. Its edge is \(3\,\mathrm{cm}\) long. Imagine, we cut the cube into small unit cubes with the edge length of \(1\,\mathrm{cm}\) and we select one of the unit cubes at random (see the picture). What is the probability of selecting a unit cube with three faces painted in green?
\( \frac{8}{27} \)
\( \frac{7}{27} \)
\( \frac{4}{27} \)
\( \frac{6}{27} = \frac{2}{9}\)

2000004702

Level: 
B
A part of a rectangle drawn on the wall is painted in yellow (see the picture). Imagine a bee landing on a random spot of the rectangle. What is the probability of the bee landing on the yellow part?
\( \frac{3}{8} \)
\( \frac{1}{3} \)
\( \frac{1}{8} \)
\( \frac{5}{8} \)

2000004405

Level: 
C
We randomly choose natural numbers from between \(1\) to \(20\) so that each choice is equally probable. Let the event \(A\) be: the chosen number is divisible by \(5\). Let the event \(B\) be: the chosen number is smaller than \(11\). Find \(P(A\mid B)\).
\( \frac{1}{5}\)
\( \frac{2}{11}\)
\( \frac{1}{4}\)
\( \frac{2}{5}\)

2000004404

Level: 
B
Two identical light bulbs are connected to the battery as shown in the electrical circuit diagram. The reliability of each of the bulbs is \(0.5\). What is the probability that the current flows through the circuit, i.e., at least one bulb is glowing? (Note: Reliability is the probability that the component will perform its intended function.)
\( 0.75\)
\( 0.5\)
\( 1\)
\( \frac{1}{4}\)

2000004403

Level: 
B
Two identical light bulbs are connected to the battery as shown in the electrical circuit diagram. The reliability of each of the bulbs is \(0.4\). What is the probability that the current flows through the circuit, i.e., both bulbs are glowing? (Note: Reliability is the probability that the component will perform its intended function.)
\(0.16\)
\(0.8\)
\(\frac{2}{5}\)
\( \frac{1}{2}\)

2000004402

Level: 
B
Peter built a maze for his pet mouse Mickey (see the floor plan in the picture). In addition, he placed some cheese in an airtight container in room B. Suppose that every time Mickey reaches a split in the maze, he is equally likely to choose any of the paths in front of him. Which of the following statements is true?
The probability that Mickey will end up in room A or C is the same.
The probability that Mickey will end up in room C is greater than for room A.
The probability that Mickey will end up in room B is the same as in case of rooms A and C.

2000004401

Level: 
B
Peter built a maze for his pet mouse Mickey (see the floor plan in the picture). In addition, he placed some cheese in an airtight container in room B. Suppose that every time Mickey reaches a split in the maze, he is equally likely to choose any of the paths in front of him. What is the probability of Mickey ending up in room B with cheese?
\( \frac{2}{3}\)
\( \frac{1}{2}\)
\( \frac{1}{3}\)
\( \frac{3}{5}\)