Probability

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.
\( \frac{\binom{16}2+\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}79 \)
\( \frac{\binom{16}2}{\binom{30}2}\doteq 0{.}28 \)
\( \frac{\binom{14}2}{\binom{30}2}\doteq 0{.}21 \)
\( \frac{\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}51 \)

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.
\( \frac{\binom{46}5 + \binom{46}4\cdot\binom41}{\binom{50}5}\doteq 0{.}96 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}}{\frac{50!}{45!}}\doteq 0{.}66 \)
\( \frac{\binom{46}5 + \binom{46}4}{\binom{50}5}\doteq 0{.}72 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}\cdot \frac{4!}{3!}}{\frac{50!}{45!}}\doteq 0{.}71 \)

1003041601

Level: 
A
The wooden cube with the edges of length \( 5\,\mathrm{cm} \) 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 least two faces painted in blue?
\( 0{.}352 \)
\( 0{.}288 \)
\( 0{.}480 \)
\( 0{.}432 \)

1003019103

Level: 
A
There are \( 30 \) students in the class, one of them is Adam. The teacher picks randomly three students to be tested. What is the probability that Adam is among them?
\( \frac{\binom{29}2}{\binom{30}3}=0{.}1 \)
\( \frac{\binom{29}2}{\binom{30}2}\doteq 0{.}9333 \)
\( \frac{\binom{29}3}{\binom{30}3}=0{.}9 \)
\( \frac{\binom31\binom{27}2}{\binom{30}{3}}\doteq 0{.}2594 \)

1003019206

Level: 
B
Adam and Eve met at the disco. They agreed to meet the next day at the same location sometime between \( 1 \) p.m. and \( 2 \) p.m. Both of them will arrive independently at random times within the hour. Adam is greatly interested in the meeting, therefore he is willing to wait for Eve even up to half an hour, while Eve is willing to wait for Adam for \( 10 \) minutes. What is the probability that they will meet during that hour?
\( \frac{19}{36}\doteq 0{.}5278 \)
\( \frac{17}{36}\doteq 0{.}4722 \)
\( \frac{11}{36}\doteq 0{.}3056 \)
\( \frac{27}{36}=0{.}75 \)

1003019205

Level: 
C
Adam and Eve met at the disco. They agreed to meet the next day at the same location sometime between \( 1 \) p.m. and \( 2 \) p.m. Both of them will arrive independently at random times within the hour and wait ten minutes for the other. What is the probability that they will not meet during that hour?
\( \frac{25}{36}\doteq 0{.}6944 \)
\( \frac{11}{36}\doteq 0{.}3056 \)
\( \frac{35}{36}\doteq 0{.}9722 \)
\( \frac{24}{36}\doteq 0{.}6667 \)

1003019204

Level: 
B
Inside a circle is inscribed a square. A point is chosen at random from inside the circle. What is the probability that this point is located also in the square?
\( \frac2{\pi}\doteq 0{.}6366 \)
\( \frac{\pi}4\doteq 0{.}7854 \)
\( \frac{\sqrt{2}}{\pi}\doteq 0{.}4502 \)
\( \frac{\sqrt{2}}{2\pi}\doteq 0{.}2251 \)