## Continuous Beam With Equal Support Reactions

**Situation**

A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length *x* is so calculated in order that the reactions at all supports shall be the same.

1. Find *x* in meters.

A. 1.319 | C. 1.217 |

B. 1.139 | D. 1.127 |

2. Find the moment at *B* in N·m.

A. -240 | C. -242 |

B. -207 | D. -226 |

3. Calculate the reactions in Newton.

A. 843.4 | C. 863.8 |

B. 425.4 | D. 827.8 |

## 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?

## Continuous Beam With a Gap and a Zero Moment in Interior Support

**Situation**

A beam of uniform cross section whose flexural rigidity *EI* = 2.8 × 10^{11} N·mm^{2}, is placed on three supports as shown. Support *B* is at small gap Δ so that the moment at *B* is zero.

1. Calculate the reaction at *A*.

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

2. What is the reaction at *B*?

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

3. Find the value of Δ.

A. 46 mm | C. 34 mm |

B. 64 mm | D. 56 mm |

## Probability that a Large Shipment is Accepted or Not Accepted due to Defective Items

**Problem**

A stationery store has decided to accept a large shipment of ball-point pens if an inspection of 20 randomly selected pens yields no more than two defective pens. Find the probability that this shipment is...

- accepted if 5% of the total shipment is defective.
- not accepted if 15% of the total shipment is defective.

## 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.

## Three Men Shoot and Only One of Them Hits the Target. Find the Probability that it was the First Man

## 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

where *x* is a discrete random variable

*P*(

*x*) = probability for

*x*occurrences

*μ*= the mean number of occurrences

## Probability: A Family of Five Children

**Problem**

A family chosen at random has 5 children. What is the probability that...

- all are girls or all are boys?
- there are 3 boys and 2 girls?
- at least 1 is a boy?

## 09 - Number of Leaps to Take to Catch the Lead

**Problem**

A cat takes 4 leaps to a dog's 3; but 2 of the dog's leaps are equivalent to 3 of the cat’s. The cat has a start of 50 leaps. How many leaps must the dog take to catch the cat?

## Number of Steps in the Escalator

**Problem**

A certain businessman, who is always in a hurry, walks up an ongoing escalator at the rate of one step per second. Twenty steps bring him to the top. Next day he goes up at two steps per second, reaching the top in 32 steps. How many steps are there in the escalator?

A. 80 | C. 50 |

B. 60 | D. 70 |