2010016902
Level:
B
Two dice are rolled. Find the probability that we get the number \(5\) at least once.
\(\frac{11}
{36}\doteq 0.3056\)
\(\frac{25}
{36}\doteq 0.6944\)
\(\frac{12}
{36}\doteq 0.3333\)
\(\frac{10}
{36}\doteq 0.2778\)
Probability
2010016901
Level:
B
Two different dice (a white die and a black die) are rolled. Find the probability that we get the number
\(4\) on the white die and a number different from \(4\) on the black die.
\(\frac{5}
{36}\doteq 0.1389\)
\(\frac{4}
{36}\doteq 0.1111\)
\(\frac{1}
{6}+\frac56\,=\,1\)
\(\frac{5}
{6}\doteq 0.8333\)
2010015505
Level:
B
The probability of a man hitting a target is \(0.7\). What is the probability that he does not hit the target twice in a row? Round the result to two decimal places.
\(0.09\)
\(0.49\)
\(0.77\)
\(0.14\)
2010015504
Level:
B
Two regular dice are thrown. Find the probability that the sum is eight or nine. The results are rounded to two decimal places.
\(\frac14 = 0.25\)
\(\frac{10}{36} = 0.28\)
\(\frac5{36} = 0.14\)
\(\frac2{11} = 0.18\)
2010015503
Level:
B
Four participants of a target shooting competition do hit the target with hitting probabilities: \(0.82\); \(0.86\); \(0.90\) and \(0.94\). What is the probability that at least one of the participants does not hit the target? Round the result to four decimal places.
\(0.4034\)
\(0.5966\)
\(0.4800\)
\(0.0002\)
2010015502
Level:
B
A set of Christmas tree lights contains \(10\) identical bulbs connected in parallel. Each of the bulbs has the reliability of \(96\,\%\). What is the probability (expressed as a percentage) that all of the bulbs will glow? Round the result to one decimal place. (Note: Reliability is the probability that the system will perform its intended function.)
\(66.5\,\%\)
\(96\,\%\)
\(66.4\,\%\)
\(92.2\,\%\)
2010015501
Level:
B
Three identical light bulbs are connected to the battery as shown in the electrical circuit diagram. The reliability of each of the bulbs is \(0.95\). What is the probability that the current flows through the circuit? Round the result to \(4\) decimal places. (Note: Reliability is the probability that the component will perform its intended function.)
\(0.9476\)
\(0.8574\)
\(0.9951\)
\(0.0475\)
2000004706
Level:
A
What is the probability of getting three heads in three coin tosses?
\( \frac{1}{8} \)
\( \frac{1}{2} \)
\( \frac{1}{6} \)
\( \frac{1}{4} \)
2000004705
Level:
A
A distracted secretary prepares three envelopes and types three different letters for three different people. Then she randomly places the letters in the prepared envelopes. What is the probability of at least two recipients receiving the right letter?
\( \frac{1}{6} \)
\( \frac{1}{3} \)
\( \frac{2}{3} \)
\( \frac{3}{6} = \frac{1}{2}\)
2000004704
Level:
A
There is a wooden cube with faces painted in green. Its edge is \(3\,\mathrm{cm}\) long. Imagine we cut the cube into small unit cubes with the edge length of \(1\,\mathrm{cm}\) and we select one of the unit cubes at random (see the picture). What is the probability of selecting an unpainted cube?
\( \frac{1}{27}\)
\( \frac{3}{27} = \frac{1}{9}\)
\( 0\)
\( \frac{1}{6}\)