Probability

9000154808

Level: 
A
Little John plays a dice game against Robin Hood. To win, he needs to get the sum of \(8\) by rolling two dice. What is the probability that he wins over Robin right on the first roll? Round your result to three decimal places.
\(0{.}139\)
\(0{.}194\)
\(0{.}806\)
\(0{.}778\)

1003019202

Level: 
B
There are fifty apples left on a tree and ten of them have worms. We pick five apples at random. What is the probability that at least one of them is without a worm?
\( 1-\frac{\binom{10}{5}}{\binom{50}{5}}\doteq 0{.}9999 \)
\( 1-\frac{\binom{10}{1}}{\binom{50}{5}}\doteq 1{.}0000 \)
\( 1-\frac{\binom{10}{1}\binom{40}{4}}{\binom{50}{5}}\doteq 0{.}5687 \)
\( 1-\frac{\binom{40}{5}}{\binom{50}{5}}\doteq 0{.}6894\)

1003019204

Level: 
B
Inside a circle is inscribed a square. A point is chosen at random from inside the circle. What is the probability that this point is located also in the square?
\( \frac2{\pi}\doteq 0{.}6366 \)
\( \frac{\pi}4\doteq 0{.}7854 \)
\( \frac{\sqrt{2}}{\pi}\doteq 0{.}4502 \)
\( \frac{\sqrt{2}}{2\pi}\doteq 0{.}2251 \)

1003019206

Level: 
B
Adam and Eve met at the disco. They agreed to meet the next day at the same location sometime between \( 1 \) p.m. and \( 2 \) p.m. Both of them will arrive independently at random times within the hour. Adam is greatly interested in the meeting, therefore he is willing to wait for Eve even up to half an hour, while Eve is willing to wait for Adam for \( 10 \) minutes. What is the probability that they will meet during that hour?
\( \frac{19}{36}\doteq 0{.}5278 \)
\( \frac{17}{36}\doteq 0{.}4722 \)
\( \frac{11}{36}\doteq 0{.}3056 \)
\( \frac{27}{36}=0{.}75 \)

1003029302

Level: 
B
The quality inspection found that \( 85\% \) of the items are without defect, exactly one defect has \( 10\% \) of the items, and the other items have more than one defect. We pick one item randomly. What is the probability that this item has at least one defect?
\( 0{.}15 \)
\( 0{.}10 \)
\( 0{.}95 \)
\( 0{.}01 \)