Probability of an Event:

The probability of an event E is P(E) = n(E)   where n means the number of ways .
                                                           n(S)
S is the sample space.

Examples:
(a)  Two coins are tossed.  What is the probability that both land tails up?
       Answer:  S = { HH, HT, TH, TT }  Only one of these events has 2 tails, so the probability is
                     2/4 = 1/2.

(b)  A card is drawn from a standard deck of playing cards.  What is the probability that it is an ace?
       Answer:  There are 52 cards in a standard deck of playing cards.  Four of them are aces.  So
                       the probability of drawing an ace is 4/52 = 1/13.

(c)  Two six-sided dice are tossed.  What is the probability that the total of the two dice is 6?
       Answer:  S =     1  2  3    4   5    6
                             1| 2  3  4    5   6    7
                             2| 3  4  5    6   7    8
                             3| 4  5  6    7   8    9
                             4| 5  6  7    8   9   10
                             5| 6  7  8    9  10  11
                             6| 7  8  9  10  11  12
                      Five of these 36 possibilities are 6's.  So the probability that the total of the two dice
                       is 6 = 5/36.

Probability of the Union of Two Events:

The probability of A or B occurring is

  P(A) U P(B) = P(A) + P(B) - P(A and B)

If A and B are mutually exclusive, then
   P(A) U P(B) = P(A) + P(B)
 

Probability of Independent Events:

If A and B are independent events,

P(A and B) = P(A) P(B)

Example:  Select 3 numbers from 1 - 15.  Find  the probability that each number is less than 7.
                  Answer:  P (N < 7) = 7 / 15
                                  So the probability that all 3 are less than 7 is (7 / 15)3 = 343 / 3375 » .102.

Probability of a Complement:

P(A’) = 1 - P(A).


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