Probability and Statistics

A box contains a mixture of red, blue, and green tokens. There are exactly $16$ red tokens in the box. The probability of randomly selecting a red token is $\frac{2}{5}$. If there are $14$ blue tokens in the box, what is the probability of randomly selecting a green token on a single draw?

A logistics officer is analyzing data from various base operations. Match each statistical description on the left with its correctly calculated value on the right.

A maintenance kit contains $12$ metric wrenches, $15$ standard wrenches, $9$ screwdrivers, and an unknown number of pliers. If the probability of randomly selecting a screwdriver from the entire kit is $\frac{1}{6}$, what is the probability of randomly selecting a standard wrench? Express your answer as a fraction in simplest form.

An artillery spotter is recording the impact distances (in meters) from a target center for five test rounds. The distances are $34$, $41$, $28$, $52$, and $40$. A sixth round is fired. If the mean distance for all six rounds is exactly $41$ meters, what was the impact distance of the sixth round?

A military supply depot receives a shipment of $400$ uniform jackets. Of these jackets, $25\%$ are size Small, $\frac{3}{8}$ are size Medium, and the remaining jackets are divided equally between size Large and size Extra-Large. If a quartermaster randomly selects one jacket from the entire shipment, what is the probability that it is a size Extra-Large jacket?

A structural mechanic is testing the tensile strength of a batch of aluminum rivets. The mean tensile strength of the first $4$ rivets tested is $410$ MPa. If the quality standard requires the mean strength of $5$ rivets to be exactly $415$ MPa, what tensile strength must the $5$ th rivet have?

A secure military facility uses three independent detection systems to monitor its perimeter. The probability that the primary radar detects an incoming drone is 0.80. The probability that the infrared system detects it is 0.90. The probability that the acoustic sensors detect it is 0.75. If a drone approaches the perimeter, what is the probability that exactly two of the three systems detect it? Express your answer as a decimal.

A quartermaster is recording the number of uniform items issued per day over an $8$-day period. The recorded numbers are $24$, $19$, $28$, $17$, $33$, $16$, $20$, and $27$. What is the median number of uniform items issued?

A damage control officer is reviewing the completion times (in minutes) for various emergency response drills. Match each statistical description on the left with its correctly calculated value on the right.

A 5-character security passcode must be created using the digits 0 through 9. The passcode must begin with an odd digit, end with an even digit, and no digit may be repeated anywhere in the passcode. How many different passcodes can be created?

A flight engineer is monitoring the fuel consumption, in gallons per hour (GPH), of a cargo aircraft during $4$ different flight legs. The consumption for the first $3$ legs was $520$, $480$, and $550$ GPH.

If the target mean fuel consumption for all $4$ legs is $510$ GPH, what must the fuel consumption be for the $4$ th leg?

A scientist records the temperature changes, in degrees Celsius, of a chemical solution during five different phases of an experiment. The recorded changes are: $-2.5$, $3.0$, $-5.5$, $4.5$, and $-1.0$. What is the range of these temperature changes?

A maintenance technician is tracking the number of work orders completed each day. Over a $5$-day work week, the technician wants to achieve a mean of $14$ completed work orders per day. If the technician completed $12$, $16$, $11$, and $13$ work orders on the first four days, how many work orders must be completed on the fifth day to exactly meet the target mean?

Match each data set to its corresponding statistical range.

An armory stores a mixture of lithium, alkaline, and nickel-metal hydride (NiMH) batteries. The probability of randomly selecting a lithium battery from the storage is $\frac{2}{5}$. If there are exactly $48$ lithium batteries in the armory, what is the total number of batteries stored?

A quartermaster is organizing a drawer of $60$ uniform patches. The drawer contains $15$ rank insignia patches, $21$ unit patches, and the remaining patches are flag patches. If one patch is randomly selected from the drawer, what is the probability of selecting a flag patch? Express your answer as a decimal.

A motor pool inventory shows that $\frac{1}{4}$ of the vehicles are heavy trucks, $\frac{1}{3}$ are light tactical vehicles, and the remaining vehicles are armored personnel carriers. If a vehicle is randomly selected for an inspection, what is the probability that it is an armored personnel carrier?

An electrician's toolbox contains $8$ red wire connectors, $14$ blue wire connectors, and $10$ green wire connectors. If the electrician randomly selects one connector without looking, what is the probability that it is NOT a blue connector?

A supply sergeant is organizing a crate of $150$ signal flares. The crate contains $50$ red flares, $40$ green flares, $36$ yellow flares, and the remaining flares are white. If a recruit randomly selects one flare from the crate without looking, what is the probability that they select a white flare? Express your answer as a decimal.

A dining facility manager is planning a special event and will randomly select one pie from a large frozen delivery. According to the shipping manifest, $\frac{1}{3}$ of the pies are apple, $\frac{1}{4}$ are cherry, $\frac{1}{5}$ are blueberry, and the rest are pecan. What is the probability that the randomly selected pie is a pecan pie?