Probability

1103164505

Level: 
B
Suppose we have a rectangular fish tank which is 4dm long, 2dm wide, and it is filled with water up to the height of 3dm. 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 5cm 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

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

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

1003164501

Level: 
B
In the house with a 7 metre high ground storey and 6 other storeys (5 metres high each), there is a lift. On each storey, it is possible to enter this lift through a glass door that is 2 metres high. The lift malfunctioned and stopped somewhere on its way. What is the probability that (at the moment of stoppage) it would not be possible to see out of the lift only the wall of the lift shaft?
0.7500
0.7838
0.7188
0.7647
0.7353
0.7568

1003158309

Level: 
C
Students of a class take a multiple choice test consisting of 10 tasks. There are 5 optional answers to each of the tasks, while only one answer is correct. One student, however, did not study for the test at all. Therefore, he circles his answers randomly, without performing any calculations. Find the probability that he will circle at least 3 correct answers. Round the result to four decimal places.
0.3222
0.8591
0.1409
0.6778

1003158308

Level: 
C
The probability that the randomly selected product is first-class quality is 0.12. Determine the probability that at least 2 out of 50 randomly selected products are first-class quality. Round the result to four decimal places.
0.9869
0.9689
0.8969
0.8699
0.9896
0.8996