Probability

1103019203

Level: 
B
The dartboard in the picture is made up of three concentric circles with radii \( 4 \), \( 6 \) and \( 8 \) cm. Assuming that a dart thrown will land randomly on the dartboard, what is the probability that it lands in the red region?
\( \frac5{16}\doteq 0{.}3125 \)
\( \frac3{4}=0{.}75 \)
\( \frac1{4}=0{.}25 \)
\( \frac9{16}\doteq 0{.}5625 \)

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?
\( 1-\frac{\binom{10}{5}}{\binom{50}{5}}\doteq 0{.}9999 \)
\( 1-\frac{\binom{10}{1}}{\binom{50}{5}}\doteq 1{.}0000 \)
\( 1-\frac{\binom{10}{1}\binom{40}{4}}{\binom{50}{5}}\doteq 0{.}5687 \)
\( 1-\frac{\binom{40}{5}}{\binom{50}{5}}\doteq 0{.}6894\)

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.
\(\frac{6} {15};\, \frac{8} {15};\, \frac{1} {15}\)
\(\frac{3} {9};\, \frac{5} {9};\, \frac{1} {9}\)
\(\frac{1} {3};\, \frac{2} {3};\, \frac{2} {3}\)
\(\frac{1} {2};\, \frac{1} {4};\, \frac{1} {4}\)

9000154802

Level: 
C
Three hundred soldiers know details related to the weapon transport to Nottingham. The probability that a soldier betrays the sheriff and tells the details to Robin Hood is \(0.01\) . This probability is fixed for all soldiers. Robin tries to find out the details on the transport by asking each soldier. Find the probability that Robin will find out details (i.e. at least one soldier tells the secret to Robin). Round your answer to three decimal places.
\(0.951\)
\(0.049\)
\(0.827\)
\(0.173\)

9000154803

Level: 
B
The probability that Robin Hood hits the target is \(0.83\). The same probability is \(0.61\) for Robin's fellow, Little John. Both Robin and John shot on the wolf. Find the probability that they will hit the wolf. Round your answer to three decimal places.
\(0.934\)
\(1.440\)
\(0.506\)
\(0.494\)

9000154804

Level: 
C
Robin Hood wants to have \(6\) children with his love Maid Marian. Find the probability that they will have \(2\) girls and \(4\) boys. The probability that one child will be a girl is \(48.79\%\) and the probability of a boy is \(51.21\%\). Round your answer to three decimal places.
\(0.246\)
\(0.222\)
\(0.015\)
\(0.016\)

9000154805

Level: 
C
A boy plays Monopoly game. He is in the jail and has to roll three times a pair of dices. To escape from the jail he needs the number six on both dices. Find the probability that he succeeds to escape the jail. Round your answer to three decimal places.
\(0.081\)
\(0.919\)
\(0.028\)
\(0.095\)

9000154806

Level: 
B
A man plays a dice game. He rolls one dice three times and to win he needs at least one number six. However, the dice is not fair. The probability of an even number is two times bigger than the probability of an odd number. Find the probability that the man wins. Suppose that all even numbers have equal probability and all odd numbers also have equal probability. Round your answer to three decimal places.
\(0.529\)
\(0.471\)
\(0.421\)
\(0.579\)

9000154807

Level: 
B
The Robin's band has \(10\) men and \(5\) women. From this group they select randomly two fellows to negotiate with the Sheriff of Nottingham. Find the probability that there will be one man and one woman in the selected pair. Round your answer to three decimal places.
\(0.476\)
\(0.952\)
\(0.325\)
\(0.675\)