Probability

1003041602

Level: 
C
A box contains \( 50 \) transistors and \( 4 \) of them are lower quality. From all transistors \( 5 \) are selected at random for inspection. What is the probability that of lower quality is at most one of the selected transistors? Round the result to two decimal places.
\( \frac{\binom{46}5 + \binom{46}4\cdot\binom41}{\binom{50}5}\doteq 0{.}96 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}}{\frac{50!}{45!}}\doteq 0{.}66 \)
\( \frac{\binom{46}5 + \binom{46}4}{\binom{50}5}\doteq 0{.}72 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}\cdot \frac{4!}{3!}}{\frac{50!}{45!}}\doteq 0{.}71 \)

1003041603

Level: 
C
There are \( 30 \) students in a class, of them are \( 14 \) girls and the rest are boys. The teacher selects two students for weekly routine help. If selection is done at random, what is the probability that these students are not two girls? Round the result to two decimal places.
\( \frac{\binom{16}2+\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}79 \)
\( \frac{\binom{16}2}{\binom{30}2}\doteq 0{.}28 \)
\( \frac{\binom{14}2}{\binom{30}2}\doteq 0{.}21 \)
\( \frac{\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}51 \)

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.
\( 0{.}6129 \)
\( 0{.}7097 \)
\( 0{.}3065 \)
\( 0{.}3548 \)

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.
\( 0{.}1169 \)
\( 0{.}1619 \)
\( 0{.}1961 \)
\( 0{.}1916 \)
\( 0{.}1196 \)
\( 0{.}1691 \)

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.
\( 0{.}6769 \)
\( 0{.}9000 \)
\( 0{.}2852 \)
\( 0{.}7148 \)
\( 0{.}8100 \)

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