Probability

1103164503

Level: 
B
An equilateral triangle with a side of 3 metres is drawn on the wall. Inside the triangle, there is a circle with the diameter of 1 metre. If a fly sits by chance in the triangle, what is the probability that it does not sit inside the circle? Round the result to 4 decimal places.
\( 0.7985 \)
\( 0.2015 \)
\( 0.8061 \)
\( 0.1939 \)

1103164504

Level: 
B
An equilateral triangle is drawn on the wall. Inside the triangle, there is a circle with the radius of \( 1 \) metre inscribed. If a fly sits by chance in the triangle, what is the probability that it does not sit inside the circle? Round the result to \( 4 \) decimal places.
\( 0.3954 \)
\( 0.6046 \)
\( 0.3023 \)
\( 0.6977 \)

1103164505

Level: 
B
Suppose we have a rectangular fish tank which is \( 4\,\mathrm{dm} \) long, \( 2\,\mathrm{dm} \) wide, and it is filled with water up to the height of \( 3\,\mathrm{dm} \). In its four bottom corners, there are jets through which a fresh air is driven into the water in specific intervals. The fresh air is driven to the distance of up to \( 5\,\mathrm{cm} \) from the tank corners. If a fish swims inside the tank, what is the probability that the fish will not be hit by the stream of bubbles, at the moment when all four jets are acting? The fish dimensions can be neglected, round the result to \( 4 \) decimal places.
\( 0.9891 \)
\( 0.0109 \)
\( 0.9984 \)
\( 0.0016 \)
\( 0.9782 \)
\( 0.0218 \)

1103164506

Level: 
B
At night, a parachutist landed on the spot \( M \), which is \( 3\,\mathrm{km} \) and \( 4\,\mathrm{km} \) away from the two straight and mutually perpendicular roads \( p \) and \( q \) respectively (see the picture). From the landing point, the parachutist walks straight in a random direction at the constant speed of \( 6\,\mathrm{km}/\mathrm{h} \). What is the probability that he reaches one of the roads in less than an hour? Round the result to \( 4 \) decimal places. \[ \] Hint: In the case of linear motion with constant speed, the speed is equal to the ratio of the displacement and the time of motion.
\( 0.5505 \)
\( 0.4495 \)
\( 0.6011 \)
\( 0.3989 \)
\( 0.3511 \)
\( 0.6489 \)

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?
\( \frac{2}{3}\)
\( \frac{1}{2}\)
\( \frac{1}{3}\)
\( \frac{3}{5}\)

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.

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.)
\(0.16\)
\(0.8\)
\(\frac{2}{5}\)
\( \frac{1}{2}\)

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.)
\( 0.75\)
\( 0.5\)
\( 1\)
\( \frac{1}{4}\)