Counting & Probability

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Counting:

Counting is the basis for the understanding of probability. It is a necessary technique for keeping up with quantities and the statistical data in everyday life. Counting is useful for finding the:

  • the number of ways,
  • the number of samples
  • the number of outcomes.
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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



Probability 101
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By: Farah Arabi