Probability

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?
\(0.220 \)
\(0.006 \)
\(0.160 \)
\(0.001 \)

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?
\( 1-\frac{\pi}4\doteq 0.2146 \)
\( \frac{\pi}4\doteq 0.7854 \)
\( \frac{\pi}{2\sqrt2}-1\doteq 0.1107\)
\( 1-\frac{\sqrt2}{\pi}\doteq 0.5498 \)

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?
\( 1-\frac{\binom{12}{6}}{\binom{60}{6}}\doteq 0.999982 \)
\( 1-\frac{\binom{12}{1}}{\binom{48}{6}}\doteq 0.999999 \)
\( 1-\frac{\binom{12}{1} \cdot \binom{48}{5} }{\binom{60}{6}}\doteq 0.589571 \)
\( \frac{\binom{12}{1}+\binom{12}{2} +\binom{12}{3}+\binom{12}{4}+\binom{12}{5} }{\binom{60}{6}}\doteq 0.000032 \)

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.
\(\frac{5} {36}\doteq 0.1389\)
\(\frac{4} {36}\doteq 0.1111\)
\(\frac{1} {6}+\frac56\,=\,1\)
\(\frac{5} {6}\doteq 0.8333\)