Probability

1003029305

Level: 
B
The production process of a particular component consists of three independent phases. Through long-term monitoring of production quality were found success rates of individual phases \( 90\% \), \( 80\% \) and \( 85\% \). If all three phases of the process are successful, the component is of good quality. What is the probability of producing a good quality component?
\( 0{.}612 \)
\( 0{.}003 \)
\( 0{.}388 \)
\( 0{.}997 \)

1003041702

Level: 
B
Product quality inspection was performed. Inspectors reported that \( 85\% \) of products have no defect, \( 8\% \) of products have exactly one defect, \( 5\% \) 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?
\( 0{.}15 \)
\( 0{.}07 \)
\( 0{.}08 \)
\( 0{.}13 \)

1003041704

Level: 
B
A set of Christmas tree lights contains \( 12 \) identical bulbs connected in parallel. Each of the bulbs has the reliability of \( 98\% \). What is the probability (expressed as a percentage) that all of the bulbs will glow? Round the result to one decimal place. (Note: Reliability is the probability that the system will perform its intended function.)
\( 78{.}5\% \)
\( 98{.}0\% \)
\( 78{.}4\% \)
\( 97{.}5\% \)

1003041705

Level: 
B
Product quality inspector checks two independent quality indicators, A and B. If the product does not comply with any of the indicators it is discarded otherwise it is accepted. The inspector reported that \( 95{.}4\% \) of the products was accepted. He also reported that \( 97{.}1\% \) of the products complied with the indicator A. How many of the products complied with the indicator B? Express the result in percentage and round it to two decimal places.
\( 98{.}25\% \)
\( 98{.}24\% \)
\( 92{.}63\% \)
\( 92{.}64\% \)

1003041706

Level: 
B
Four participants of a target shooting competition do hit the target with hitting probabilities: \( 0{.}80 \); \( 0{.}85 \); \( 0{.}90 \) and \( 0{.}95 \). What is the probability that just one of the participants does hit the target? Round the result to four decimal places.
\( 0{.}0057 \)
\( 0{.}0056 \)
\( 0{.}9999 \)
\( 0{.}9998 \)

1003041707

Level: 
B
Four participants of a target shooting competition do hit the target with hitting probabilities: \( 0{.}80 \); \( 0{.}85\); \( 0{.}90 \) and \( 0{.}95 \). What is the probability that at least one of the participants does hit the target? Round the result to four decimal places.
\( 0{.}9999 \)
\( 0{.}9998 \)
\( 0{.}0057 \)
\( 0{.}0056 \)

1003164501

Level: 
B
In the house with a \( 7 \) metre high ground storey and \( 6 \) other storeys (\( 5 \) metres high each), there is a lift. On each storey, it is possible to enter this lift through a glass door that is \( 2 \) metres high. The lift malfunctioned and stopped somewhere on its way. What is the probability that (at the moment of stoppage) it would not be possible to see out of the lift only the wall of the lift shaft?
\( 0.7500 \)
\( 0.7838 \)
\( 0.7188 \)
\( 0.7647 \)
\( 0.7353 \)
\( 0.7568 \)

1003164502

Level: 
B
Suppose the points \( A \) and \( B \) are randomly placed on a circle with a radius \( r \). What is the probability that the distance between \( A \) and \( B \) (length of the chord \( AB \)) is at least \( r \)?
\( \frac23 \)
\( \frac13 \)
\( \frac16 \)
\( \frac56 \)
\( \frac12 \)

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?
\( \frac5{16}\doteq 0{.}3125 \)
\( \frac3{4}=0{.}75 \)
\( \frac1{4}=0{.}25 \)
\( \frac9{16}\doteq 0{.}5625 \)

1103041703

Level: 
B
Three identical light bulbs are connected to the battery as shown in the electrical circuit diagram. The reliability of each of the bulbs is \( 0{.}95 \). What is the probability that the current flows through the circuit? Round the result to \( 4 \) decimal places. (Note: Reliability is the probability that the component will perform its intended function.)
\( 0{.}9951 \)
\( 0{.}8574 \)
\( 0{.}9476 \)
\( 0{.}9500 \)