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.
 

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

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

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

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?
 

Problem
In a 5-card poker hand, what is the probability that all 5 are of the same suit?
 

Probability
For outcomes that are equally likely to occur:

If the probability of an event to happen is p and the probability for it to fail is q, then