2010016904
Level:
B
Four dice are thrown. What is the probability that the sum is less than \( 6 \)?
\(\frac{5}
{6^4}\doteq 0.0039\)
\(1-\frac{5}
{6^4}\doteq 0.9961\)
\(\frac{2}
{6^4}\doteq 0.0015\)
\(\frac{8}
{6^4}\doteq 0.0062\)
Probability
2010016905
Level:
B
There are sixty apples left on a tree and twelve of them have worms. We pick six apples at random. What is the probability that at least one of them is without a worm?
\( 1-\frac{\binom{12}{6}}{\binom{60}{6}}\doteq 0.999982 \)
\( 1-\frac{\binom{12}{1}}{\binom{48}{6}}\doteq 0.999999 \)
\( 1-\frac{\binom{12}{1} \cdot \binom{48}{5} }{\binom{60}{6}}\doteq 0.589571 \)
\( \frac{\binom{12}{1}+\binom{12}{2} +\binom{12}{3}+\binom{12}{4}+\binom{12}{5} }{\binom{60}{6}}\doteq 0.000032 \)
2010016906
Level:
B
Inside a square is inscribed a circle. A point is chosen at random from inside the square. What is the probability that this point is not located also in the circle?
\( 1-\frac{\pi}4\doteq 0.2146 \)
\( \frac{\pi}4\doteq 0.7854 \)
\( \frac{\pi}{2\sqrt2}-1\doteq 0.1107\)
\( 1-\frac{\sqrt2}{\pi}\doteq 0.5498 \)
2010016907
Level:
B
Product quality inspection was performed. Inspectors reported that \( 78\% \) of products have no defect, \( 10\% \) of products have exactly one defect, \( 6\% \) of products have exactly two defects and other products have more than two defects. What is the probability that a product selected at random has at least one defect?
\(0.220 \)
\(0.006 \)
\(0.160 \)
\(0.001 \)
2010017903
Level:
B
Suppose that the success rate of one specific medical treatment is \(80\,\%\). If the treatment is given to \(10\) new patients, what is the probability that it is effective in at least \(8\) of them? Round the result to four decimal places.
\(0.6778\)
\(0.1076\)
\(0.4094\)
\(0.1600\)
9000138301
Level:
B
Two dices are rolled. Find the probability that the sum of the numbers on both dices does not
exceed the number \(6\).
\(\frac{15}
{36}\doteq 0{.}4167\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{18}
{36}=0{.}5\)
\(\frac{12}
{36}\doteq 0{.}3333\)
9000138302
Level:
B
Two dices are rolled. Find the probability that we get either at least one number
\(6\) or the sum of the
numbers on both dices is \(8\).
\(\frac{14}
{36}\doteq 0{.}3889\)
\(\frac{16}
{36}\doteq 0{.}4444\)
\(\frac{11}
{36}\doteq 0{.}3056\)
\(\frac{5}
{36}\doteq 0{.}1389\)
9000138304
Level:
B
Two different dice (a white die and a black die) are rolled. Find the probability that we get the number
\(3\) on the black die and a
number different from \(3\)
on the white die.
\(\frac{5}
{36}\doteq 0{.}1389\)
\(\frac{3}
{36}\doteq 0{.}0833\)
\(\frac{6}
{36}\doteq 0{.}1667\)
\(\frac{1}
{36}\doteq 0{.}0278\)
9000138306
Level:
B
Two dice are rolled. Find the probability that we get the number \(3\) at least once.
\(\frac{11}
{36}\doteq 0{.}3056\)
\(\frac{3}
{36}\doteq 0{.}0833\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{12}
{36}\doteq 0{.}3333\)
9000138307
Level:
B
Two dice are rolled. What is the probability of getting \(10\) as the product of the two dice.
\(\frac{2}
{36}\doteq 0{.}0556\)
\(\frac{10}
{36}\doteq 0{.}2778\)
\(\frac{1}
{36}\doteq 0{.}0278\)
\(\frac{5}
{36}\doteq 0{.}1389\)