## 04 - A Point in a Square to Subtend an Obtuse Angle to Adjacent Corners

**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?

**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?

**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...

- exactly 3 of them will receive the correct shoe size?
A. 1/16 C. 1/12 B. 1/24 D. 0 - all of them will receive the correct shoe size?
A. 1/16 C. 1/12 B. 1/24 D. 0 - none of them will receive the correct shoe size
A. 3/8 C. 1/16 B. 23/24 D. 5/12

01 - 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
*P*(*x*) = probability for *x* occurrences

*μ* = the mean number of occurrences

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

- Read more about Poisson Probability Distribution
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