Probability

What is the Chance of Rain: Local vs Federal Forecasts

Problem
The local weather forecaster says “no rain” and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is 3/4. With no other data available, what is the chance of rain?

A.   3/5 C.   1/6
B.   1/4 D.   5/12

 

Survival Probability Of The 6th Fly that Attempt To Pass A Spider

Problem
A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?

A.   1/2 C.   3/4
B.   1/4 D.   2/3

 

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

 

Probability That Exactly 1 is Defective in Getting 2 Cell Phones

Problem
A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects 2 cell phones at random without replacement. What is the probability that exactly 1 is defective?

A.   0.0190 C.   0.0390
B.   0.0490 D.   0.0290

 

Expected Profit for the Acceptance of Estimate of an Engineering Company

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

 

Duel of Two 50% Marksmen: Odds in favor of the man who shoots first

Problem
Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?

A.   1/3 C.   2/3
B.   1/2 D.   1/4

 

Probability That A Randomly Selected Chord Exceeds The Length Of The Radius Of Circle

Situation
If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

  1. Assume that the distance of the chord from the center of the circle is uniformly distributed.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  2. Assume that the midpoint of the chord is evenly distributed over the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  3. Assume that the end points of the chord are uniformly distributed over the circumference of the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75

 

Probability that a Point Inside a Square Will Subtend an Obtuse Angle to Adjacent Corners of the Square

Problem
Point P is randomly chosen inside the square ABCD. Lines AP and PB are then drawn. What is the probability that angle APB is obtuse?
 

1 - Probability for cars to pass through a point on road in a 5-minute period

Problem
The number of cars passing a point on a road may be modelled by Poisson distribution. At an average, 4 cars enters the Caibaan Diversion Road in Tacloban City every 5 minutes. Find the probability that in a 5-minute period (a) two cars go past and (b) fewer than 3 cars go past.
 

Poisson Probability Distribution

The number of occurrences in a given time interval or in a given space can be modeled using Poisson Distribution if the following conditions are being satisfied:

  • The events occur at random.
  • The events are independent from one another.
  • The average rate of occurrences is constant.
  • There are no simultaneous occurrences.

 

The Poisson distribution is defined as

$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$

where x is a discrete random variable

P(x) = probability for x occurrences
μ = the mean number of occurrences

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