Probability

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

1003158408

Level: 
C
The class consists of \( 10\,\% \) long haired boys, \( 30\,\% \) short haired boys, \( 50\,\% \) long haired girls and \( 10\,\% \) short haired girls. We choose one of the students from the class randomly. Find the probability that the student has long hair if you know he is a boy.
\( 0{.}25 \)
\( 0{.}40 \)
\( 0{.}10 \)
\( 0{.}03 \)

1003158407

Level: 
C
The long-term records of a car dealer show that a customer getting a new car buys within special equipment offers a parking assistant system (PAS) with the probability \( 50\,\% \) and that he buys a xenon flashlight with the probability \( 20\,\% \). Both items of special equipment (PAS and xenon lamps) are purchased by the customer with the probability \( 10\,\% \). What is the probability that the customer bought xenon lamps if you know he bought PAS?
\( 20\,\% \)
\( 60\,\% \)
\( 10\,\% \)
\( 80\,\% \)