Probability

2000004405

Level: 
C
We randomly choose natural numbers from between \(1\) to \(20\) so that each choice is equally probable. Let the event \(A\) be: the chosen number is divisible by \(5\). Let the event \(B\) be: the chosen number is smaller than \(11\). Find \(P(A\mid B)\).
\( \frac{1}{5}\)
\( \frac{2}{11}\)
\( \frac{1}{4}\)
\( \frac{2}{5}\)

9000138303

Level: 
C
Two dice are rolled. Find the probability that we get the number \(6\) on just one of the dice and the sum of the numbers on both dice is \(8\).
\(\frac{2} {36}\doteq 0{.}0556\)
\(\frac{5} {36}\doteq 0{.}1389\)
\(\frac{11} {36}\doteq 0{.}3056\)
\(\frac{14} {36}\doteq 0{.}3889\)

9000138305

Level: 
C
Two different dices (a white dice and a black dice) are rolled. We get the sum of the numbers on both dices \(6\). Find the probability that there is an even number on the black dice.
\(\frac{2} {5}=0{.}4\)
\(\frac{5} {36}\doteq 0{.}1389\)
\(\frac{5} {18}\doteq 0{.}2778\)
\(\frac{13} {36}\doteq 0{.}3611\)

9000138308

Level: 
C
Two different dices (a white dice and a black dice) are rolled. The sum of the numbers on both dices is \(8\). Find the probability that there is \(4\) on the black dice.
\(\frac{1} {5}=0{.}2\)
\(\frac{1} {4}=0{.}25\)
\(\frac{6} {36}\doteq 0{.}1667\)
\(\frac{11} {36}\doteq 0{.}3056\)

9000154801

Level: 
C
There are six money transports through the Sherwood forest. Robin Hood knows that two of the transports are secured by soldiers. Find the respective probabilities that if Robin's band attacks two random transports, then none, one and both transports will be secured by the soldiers.
\(\frac{6} {15};\, \frac{8} {15};\, \frac{1} {15}\)
\(\frac{3} {9};\, \frac{5} {9};\, \frac{1} {9}\)
\(\frac{1} {3};\, \frac{2} {3};\, \frac{2} {3}\)
\(\frac{1} {2};\, \frac{1} {4};\, \frac{1} {4}\)