Probability

1003029206

Level: 
C
In the hospital, \( 22 \) boys and \( 18 \) girls were born in one month. Babies were listed in the register by their date of birth. Find the probability that there are at least three boys in the first five places of the register. The results are rounded to four decimal places.
\( \frac{\binom{22}3\cdot\binom{18}2+\binom{22}4\cdot\binom{18}1+\binom{22}5\cdot\binom{18}0}{\binom{40}5} = 0{.}5982 \)
\( \frac{\binom{22}3+\binom{22}4+\binom{22}5}{\binom{40}5} = 0{.}0535 \)
\( \frac{22^3\cdot18^2+22^4\cdot18^1+22^5\cdot18^0}{40^5}=0{.}1252 \)
\( \frac{\binom{22}3\cdot\binom{18}2+\binom{22}4\cdot\binom{18}1+\binom{22}5\cdot\binom{18}0}{40^5} = 0{.}0038 \)

1003029205

Level: 
C
In the hospital, \( 22 \) boys and \( 18 \) girls were born in one month. Babies were listed in the register by their date of birth. Find the probability that there are two boys and three girls in the first five places of the register. The results are rounded to four decimal places.
\( \frac{\binom{22}2\cdot\binom{18}3}{\binom{40}5}=0{.}2865 \)
\( \frac{\binom{22}2\cdot\binom{18}3}{\frac{40!}{35!}}=0{.}0024 \)
\( \frac{22^2\cdot18^3}{40^5} = 0{.}0276 \)
\( \frac{\binom{22}3\cdot\binom{18}2}{\frac{40!}{35!}}=0{.}0030 \)

1003029204

Level: 
C
A class consists of \( 50 \) students including twins, Mark and Martin. For an exam students are randomly divided into two equally sized subgroups. Find the probability that Mark and Martin will be in the same subgroup. The results are rounded to two decimal places.
\( \frac{\binom{48}{23}+\binom{48}{25}}{\binom{50}{25}}=0{.}49 \)
\( \frac{\binom{48}{23}}{\binom{50}{25}}=0{.}24 \)
\( \frac{2\cdot\binom{48}{24}}{\binom{50}{25}}=0{.}51 \)
\( \frac{\binom{49}{24}}{\binom{50}{25}}=0{.}50 \)

1003029203

Level: 
C
Three dice are thrown together. Find the probability that three different outcomes are rolled. Results are rounded to two decimal places.
\( \frac{\binom61\cdot\binom51\cdot\binom41}{6^3}=0{.}56 \)
\( \frac{\binom61+\binom51+\binom41}{6^3}=0{.}07 \)
\( \frac{\binom66\cdot\binom65\cdot\binom64}{6^3}=0{.}42 \)
\( \frac{\binom66+\binom65+\binom64}{6^3}=0{.}10 \)

1003029202

Level: 
A
In a set of \( 100 \) items, \( 15 \) are defective. We pick randomly \( 10 \) items from this set. First eight items were not defective. Find the probability that the ninth item selected is not defective too. Results are rounded to two decimal places.
\( \frac{77}{92}=0{.}84 \)
\( \frac{85}{92}=0{.}92\)
\( \frac{15}{92}=0{.}16 \)
\( \frac7{92}=0{.}08 \)

1003029201

Level: 
A
Three dice are thrown together. Let \( A \) be the event “the sum is \( 5 \)” and \( B \) be the event “the sum is \( 16 \)”. Which of the following statements is true?
Events \( A \) and \( B \) have the same probability of occurrence.
Event \( A \) is more likely to occur than event \( B \).
Event \( B \) is more likely to occur than event \( A \).

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.
\( 0{.}9999 \)
\( 0{.}9998 \)
\( 0{.}0057 \)
\( 0{.}0056 \)

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.
\( 0{.}0057 \)
\( 0{.}0056 \)
\( 0{.}9999 \)
\( 0{.}9998 \)

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.
\( 98{.}25\% \)
\( 98{.}24\% \)
\( 92{.}63\% \)
\( 92{.}64\% \)

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.)
\( 78{.}5\% \)
\( 98{.}0\% \)
\( 78{.}4\% \)
\( 97{.}5\% \)