Some Important Results

                                        _       

# We have P(A) = 1 -  P(A),

    therefore, P(A) ≤ 1.           _

                                 {Since P(A) ≥ 0,}    

                                    _

# P(Φ) = 0, since Φ = (S) and 

                  _

   P(Φ) = P(S) = 1- P(S) = 1-1 = 0 

# If in an experiment with n equally likely (and exhaustive) outcomes, m outcomes are favourable to an event A,      then probability of an event A is defined simply as 

                  P(A) = The number of possible outcomes of count as A 

                                   The total number of possible outcomes    

# For every event A in S, P(A) ≥ 0.

#  For every event A in S, 0 ≤ P(A) ≤ 1.

# Probability of an impossible event is always zero i.e.,

    P(Φ) = 0

# For the sure event or certain event, P(S) = 1. 

ILLUSTRATIONS

Experiment 1:	A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a king?
Probability:	P(not king)  =  1  -  P(king)    =  1  -   4  52    =  48 52    =  12 13

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Experiment 2:	A single 6-sided die is rolled. What is the probability of rolling a number that is not 4?
Probability:	P(not 4)  =  1  -  P(4)    =  1  -  1 6    =  5 6

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Experiment 3:	A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a club?
Probability:	P(not club)  =  1  -  P(club)    =  1  -  13 52    =  39 52    =  3 4

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Experiment 4:	A glass jar contains 20 red marbles. If a marble is chosen at random from the jar, what is the probability that it is not red?
Probability:	P(not red)  =  1  -  P(red)    =  1  -  1    =  0   Note: This is an impossible event.

Experiment 6:	A spinner has 4 equal sectors colored yellow, blue, green and red. What is the probability of landing on a sector that is not red after spinning this spinner?
Sample Space:	{yellow, blue, green, red}
Probability:	P(not red)  =  1  -  P(red)    =  1  -  1 4    =  3 4

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Summary:

The probability of an event is the measure of the chance that the event will occur as a result of the experiment. The probability of an event A, symbolized by P(A), is a number between 0 and 1, inclusive, that measures the likelihood of an event in the following way: If P(A) > P(B) then event A is more likely to occur than event B. If P(A) = P(B) then events A and B are equally likely to occur. If event A is impossible, then P(A) = 0. If event A is certain, then P(A) = 1. The complement of event A is .     P() = 1 - P(A)

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