C

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.
\( 0{.}9869 \)
\( 0{.}9689 \)
\( 0{.}8969 \)
\( 0{.}8699 \)
\( 0{.}9896 \)
\( 0{.}8996 \)

1003158307

Level: 
C
Suppose that the success rate of one specific medical treatment is \( 90\,\% \). If the treatment is given to \( 20 \) new patients, what is the probability that it is effective in at least \( 18 \) of them? Round the result to four decimal places.
\( 0{.}6769 \)
\( 0{.}9000 \)
\( 0{.}2852 \)
\( 0{.}7148 \)
\( 0{.}8100 \)

1003158302

Level: 
C
What is the probability that among \( 10 \) boys from a class born in the same year (\( 365 \) days) there are at least two having the same birthday? Round the result to four decimal places.
\( 0{.}1169 \)
\( 0{.}1619 \)
\( 0{.}1961 \)
\( 0{.}1916 \)
\( 0{.}1196 \)
\( 0{.}1691 \)

1003158301

Level: 
C
A deck of playing cards contains \( 4 \) aces, \( 12 \) face cards and \( 16 \) number cards. If you draw two cards, what is the probability that exactly one of the drawn cards is an ace or exactly one of the drawn cards is a face? Round the result to four decimal places.
\( 0{.}6129 \)
\( 0{.}7097 \)
\( 0{.}3065 \)
\( 0{.}3548 \)

1003086009

Level: 
C
The solution set of the equation \( \sin x + \cos x = 0 \) for \( x\in\mathbb{R} \) is:
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{3\pi}4+2k\pi;\frac{7\pi}4+2k\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{3\pi}4+2k\pi\right\} \)
\( \mathbb{R} \)
\( \emptyset \)