Probability

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?
\( \frac{\binom{29}2}{\binom{30}3}=0{.}1 \)
\( \frac{\binom{29}2}{\binom{30}2}\doteq 0{.}9333 \)
\( \frac{\binom{29}3}{\binom{30}3}=0{.}9 \)
\( \frac{\binom31\binom{27}2}{\binom{30}{3}}\doteq 0{.}2594 \)

1003029201

Level: 
A
Three dice are thrown together. Let \( A \) be the event “the sum is \( 5 \)” and \( B \) be the event “the sum is \( 16 \)”. Which of the following statements is true?
Events \( A \) and \( B \) have the same probability of occurrence.
Event \( A \) is more likely to occur than event \( B \).
Event \( B \) is more likely to occur than event \( A \).

1003029202

Level: 
A
In a set of \( 100 \) items, \( 15 \) are defective. We pick randomly \( 10 \) items from this set. First eight items were not defective. Find the probability that the ninth item selected is not defective too. Results are rounded to two decimal places.
\( \frac{77}{92}=0{.}84 \)
\( \frac{85}{92}=0{.}92\)
\( \frac{15}{92}=0{.}16 \)
\( \frac7{92}=0{.}08 \)

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?
\( 0{.}352 \)
\( 0{.}288 \)
\( 0{.}480 \)
\( 0{.}432 \)