# Opportunity Formulas and Example Problems

Odds Formula – Everyone who is playing or betting wants to win. By using the theory of probability introduced by Pascal, Leibniz, Fermat, and James Bernoulli, one can guess how likely an event is to occur. Although it is not necessarily 100% successful, of course it will be very helpful for you to be able to win the game.

## Application of Opportunities

As well as in games where betting is concerned, there are many other uses of opportunity. Along with the development of the theory of opportunity, it allows its use in various fields related to probability events such as weather forecasting and stock investment. To calculate the probability of various events, you can use certain mathematical rules to make the calculation easier. You can find out how to calculate the probability of an event studying this material in depth.

## Application of Opportunities Odds Formula – Multiplication Rule

### Example 1

Hendra wants to travel from city “A” to city C via town B. From city A to town B there are two ways and from town B to C there are 3 ways, as in the illustration below. City A — 2 ways —> town B, town B — 3 ways —> City C How many ways can it be taken to get from city A to city C? Ans: There are many ways to travel from city A to city B there are 2 ways. There are many ways to travel from city B to city C there are 3 ways.

### Example 2 (Opportunity Formulas)

Many alternative routes from city A to city B have 2 flight routes, while many alternative routes from city B to C have 4 road routes. Adi will travel back and forth from city A to city C.

1. Define the many different routes that Adi might take to get from city A to city C via city B!
2. Define the many different routes that Adi might take back from city C to city A via city B provided he doesn’t use the same route as he went!
3. Specify many different routes that Adi might be able to take if Adi is traveling from city A to city C via city B round trip and not using the same route!

jawab: City A — 2 ways —> town B (AB = 2 ways) town B — 4 ways —> Kota C (BC = 4 ways)

1. AB x BC = 2 x 4 = 8 routes.
2. Many different routes return from city C to city A via city B on the condition that they do not use the same route when going is: (BC-1) x (AB-1) = (4-1) x (2-1) = 3 routes
3. Many different routes commuting from city A to city C via city B without using the same route are: AB x BC x (BC-1) x (AB-1) = 2 x 4 x 3 x 1 = 24 roads