C

9000154801

Level: 
C
There are six money transports through the Sherwood forest. Robin Hood knows that two of the transports are secured by soldiers. Find the respective probabilities that if Robin's band attacks two random transports, then none, one and both transports will be secured by the soldiers.
\(\frac{6} {15};\, \frac{8} {15};\, \frac{1} {15}\)
\(\frac{3} {9};\, \frac{5} {9};\, \frac{1} {9}\)
\(\frac{1} {3};\, \frac{2} {3};\, \frac{2} {3}\)
\(\frac{1} {2};\, \frac{1} {4};\, \frac{1} {4}\)

9000154802

Level: 
C
Three hundred soldiers know details related to the weapon transport to Nottingham. The probability that a soldier betrays the sheriff and tells the details to Robin Hood is \(0.01\) . This probability is fixed for all soldiers. Robin tries to find out the details on the transport by asking each soldier. Find the probability that Robin will find out details (i.e. at least one soldier tells the secret to Robin). Round your answer to three decimal places.
\(0.951\)
\(0.049\)
\(0.827\)
\(0.173\)

9000154804

Level: 
C
Robin Hood wants to have \(6\) children with his love Maid Marian. Find the probability that they will have \(2\) girls and \(4\) boys. The probability that one child will be a girl is \(48.79\%\) and the probability of a boy is \(51.21\%\). Round your answer to three decimal places.
\(0.246\)
\(0.222\)
\(0.015\)
\(0.016\)

9000154805

Level: 
C
A boy plays Monopoly game. He is in the jail and has to roll three times a pair of dices. To escape from the jail he needs the number six on both dices. Find the probability that he succeeds to escape the jail. Round your answer to three decimal places.
\(0.081\)
\(0.919\)
\(0.028\)
\(0.095\)

9000153901

Level: 
C
Find the number of ways how to distribute \(8\) identical balls among \(5\) persons so that each of them gets at least one ball.
\(\left({7\above 0.0pt 3}\right) = 35\)
\(5^{3} = 125\)
\(\left({12\above 0.0pt 5} \right) = 792\)
\(\left({12\above 0.0pt 8} \right) = 495\)

9000150502

Level: 
C
Two hotels and a lake are in a satellite photo. The distance between the hotels is \(400\, \mathrm{m}\) which is \(4\, \mathrm{cm}\) in the photo. The area of the lake in the photo is \(30\, \mathrm{cm}^{2}\). Find the real area of the lake.
\(3\cdot 10^{5}\, \mathrm{m}^{2}\)
\(3\cdot 10^{1}\, \mathrm{m}^{2}\)
\(3\cdot 10^{3}\, \mathrm{m}^{2}\)
There is not enough information to solve this problem.

9000150504

Level: 
C
The object \(y\) is projected using a lens with foci at \(F\) and \(F'\). The focal length of the lens (the distance from the focus to the lens) \(f = 20\, \mathrm{cm}\). The distance from the object \(y\) to the lens \(a = 60\, \mathrm{cm}\). Find the distance from the lens to the image \(y'\).
\(30\, \mathrm{cm}\)
\(600\, \mathrm{cm}\)
\(\frac{20} {3} \, \mathrm{cm}\)
\(25\, \mathrm{cm}\)

9000153302

Level: 
C
A student performed repeated measurements of a length (in meters) and evaluated the main statistical characteristics: mean, standard deviation, variance and the coefficient of variation. Which of these characteristics is dimensionless?
coefficient of variation
variance
standard deviation
mean