Probability

2010020103

Level: 
A
Two dice are thrown at the same time. Which of the following statements is true?
The probability that we get the sum \(9\) is the same as the probability that we obtain the sum \(5\).
The probability that we get the sum \(9\) is two times greater than the probability that we obtain the sum \(5\).
The probability that we get the sum \(9\) is the highest possible.
None of the above is true.

2010013606

Level: 
A
In a set of \( 200 \) items, \( 20 \) are defective. We pick randomly \( 10 \) items from this set. First nine items were not defective. Find the probability that the tenth item selected is not defective too. Results are rounded to three decimal places.
\( \frac{171}{191}\doteq 0.895 \)
\( \frac{180}{191}\doteq 0.942 \)
\( \frac{180}{200}\doteq 0.9\)
\( \frac{1}{171}\doteq 0.006 \)

2010013605

Level: 
A
The wooden cube with the edges of length \( 4\,\mathrm{cm} \) has faces painted in blue. Suppose we cut the cube into small unit cubes (the edge length is \( 1\,\mathrm{cm}\)) and select one of the unit cubes at random. What is the probability that the selected cube has at most one face painted in blue?
\( 0.5 \)
\( 0.375 \)
\( 0.438 \)
\( 0.75 \)

2010013603

Level: 
A
There are \( 28 \) students in the class, one of them is Boris. The teacher picks randomly four students to be tested. What is the probability that Boris is among them?
\( \frac{\binom{27}3}{\binom{28}4}\doteq 0.143 \)
\( \frac{\binom{27}4}{\binom{28}4}\doteq 0.857 \)
\( \frac{\binom{27}3}{\binom{28}3}\doteq 0.893 \)
\( \frac{\binom{27}{3}\binom{4}1}{\binom{28}{4}}\doteq 0.571 \)

2010013601

Level: 
A
Little John plays a dice game against Robin Hood. To win, he needs to get the sum of \(7\) by rolling two dice. What is the probability that he wins over Robin right on the first roll? Round your result to three decimal places.
\(0.167\)
\(0.833\)
\(0.083\)
\(0.139\)

2010017903

Level: 
B
Suppose that the success rate of one specific medical treatment is \(80\,\%\). If the treatment is given to \(10\) new patients, what is the probability that it is effective in at least \(8\) of them? Round the result to four decimal places.
\(0.6778\)
\(0.1076\)
\(0.4094\)
\(0.1600\)