# Counting & Probability

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## Probability:

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence represented by: P(event)=….. as a percentage decimal fraction..

Probabilities range between 0 and 1, inclusive: __<__ P (event) __<__ 1.

- An event with a probability of 1 can be considered a certainty, because there are no other options.
- An event with a probability of 0 can be considered an impossibility.

1. In its simplest form, probability can be expressed as the number of occurrences of a targeted event divided by the number of occurrences *plus* the total of possible outcomes:

P(event) = (# of occurrences of a targeted event)/(# of total possible occurrences)

2. The probability of the simultaneous occurrences of two **independent events** is the product of the probabilities of each event:

**P(A and B) = P(A) . P(B)**

3. If the events A and B cannot occur simultaneously, the addition rule becomes:

**P(A or B) = P(A) + P(B) **

Example: 6th B includes 25 students:

* 3 with blonde hair (light hair)

* 9 with black hair (dark hair)

*13 with brown hair (dark hair)

No student can have dark and light hair at the same time, A new teacher chooses randomly a volunteer for his experiment from the student list. What is the probability that he will choose a student with dark hair?

P (brown or black)= **P(Brown) + P(Black)= 9/25+13/25=22/25= 0.88 **