Probability That 1, 2, 3, 4 of the Recruits Will Receive the Correct Size of Boots

Situation
Four army recruits went to the supply room to get their military boots. Their shoe sizes were 7, 8, 9 & 10. The supply officer, after being informed of their sizes, prepared the four pairs of boots they need. If the boots are handed to each of the four recruits at random, what is the probability that...

  1. exactly 3 of them will receive the correct shoe size?
    A.   1/16 C.   1/12
    B.   1/24 D.   0

     

  2. all of them will receive the correct shoe size?
    A.   1/16 C.   1/12
    B.   1/24 D.   0

     

  3. none of them will receive the correct shoe size
    A.   3/8 C.   1/16
    B.   23/24 D.   5/12

 

11 - Distance Traveled By A Messenger From Rear To Front Then Back To Rear Of A Marching Battalion

Problem
A battalion, 20 miles long, advances 20 miles. During this time, a messenger on a horse travels from the rear of the battalion to the front and immediately turns around, ending up precisely at the rear of the battalion upon the completion of the 20-mile journey. How far has the messenger traveled?
 

10 - Messenger Going From Front To Rear Then To Front Of A Marching Army Column

Problem
An army of troops is marching along a road at 5 kph. A messenger on horseback was sent from the front to the rear of the column and returns immediately back. The total time taken being 10 minutes. Assuming the messenger rides at the rate of 10 kph, determine the length of the column.
 

Number of Hours for Pipe to Fill the Tank if the Drain is Closed

Problem 1
A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Problem 2
A pipe can fill a tank in 4 hours if the drain is open. The tank is initially empty. If the pipe runs with the drain open for 1 hour and the pipe is then closed, the tank will be emptied in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Answer Key

 

Problem
The following interior angles (in degree) of a triangular traverse were measured with the same precision.
 

Angle Value No. of Measurement
A 41 2
B 77 6
C 63 2

 

What is the most probable value of angle C, in degrees?
 

A.   62.423° C.   62.571°
B.   62.874° D.   62.745°

 

Problem
An engineering company prepares an estimate for a job. The cost of preparing the estimate is Php10,000. The amount of profit over and above the Php10,000 is Php25,000 if their estimate is accepted. The probability that their estimate will be accepted 0.7 and the probability that their estimate will not be accepted is 0.3. What is the expected profit?

A.   Php12,500 C.   Php14,500
B.   Php13,500 D.   Php10,500

 

Problem
A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

A.   2π ft/min C.   3π ft/min
B.   4π ft/min D.   5π ft/min