Probability

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.
\( 0{.}3222 \)
\( 0{.}8591 \)
\( 0{.}1409 \)
\( 0{.}6778 \)

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?
\( 20\,\% \)
\( 60\,\% \)
\( 10\,\% \)
\( 80\,\% \)

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.
\( 0{.}25 \)
\( 0{.}40 \)
\( 0{.}10 \)
\( 0{.}03 \)

1103158402

Level: 
C
We roll red and yellow dice. Let the event $A$ be: On the red die a number greater than $2$ is rolled. And let the event $B$ be: The sum of points rolled on both dice is greater than $6$. Find \( P(A|B) \). (Note: In the table the sums of points on both dice are listed.)
\( \frac34 \)
\( \frac12 \)
\( \frac67 \)
\( \frac14 \)

1103158403

Level: 
C
A box (see the picture) contains \( 5 \) red balls and \( 7 \) green balls which are marked with numbers. A ball is drawn uniformly at random from the box. Find the probability that the ball is marked with even number given that the ball is red. (Round the result to two decimal places.)
\( 0{.}60 \)
\( 0{.}50 \)
\( 0{.}83 \)
\( 0{.}25 \)

1103158404

Level: 
C
A box (see the picture) contains \( 5 \) red balls and \( 7 \) green balls which are marked with numbers. A ball is drawn uniformly at random from the box. Let the event $A$ be: The drawn ball is green. And let the event $B$ be: The drawn ball is marked with the number which is greater than $6$. Find \( P(A|B) \). (Round the result to two decimal places.)
\( 0{.}50 \)
\( 0{.}43 \)
\( 0{.}25 \)
\( 0{.}83 \)