LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

PROBABILITY OF OCCURRENCE

**Probability
of Occurrence of an Event (Classical Definition) –**

**In a random experiment, let S be the sample space and E be
the event. Then, E ⊆ S. The probability of occurrence of E is
defined as –**

** Number of distinct
elements in E n (E)**

** P(E) = ------------------------------- = ---------**

** Number of distinct
elements in S n (S)**

**Some Examples –**

**1)
Tossing a Coin –**

**When
we toss a coin, the upper face of it shows either a head (H) or a tail (T)**

**So, S = {H, T}**

**When
two coins are tossed simultaneously, we have –**

** S = {HH, HT, TH, TT}**

**2)
Throwing a Die –**

**A
die is a solid cube having 6 faces marked 1, 2, 3, 4, 5, and 6 or having 1, 2,
3, 4, 5, 6 dots **

**In
throwing a die, the outcome is the number or number of dots appearing on the
upper most face.**

**The
plural of die is dice. When a die is thrown, we have S = {1, 2, 3, 4, 5, 6}**

**3) Drawing Cards From a, Well Shuffled Pack of
52 cards :-**

**A
pack of playing cards has in all 52 cards**

**(i)
It has 13 cards of each of the four suits, namely Spades, Clubs, Hearts, and
Diamonds**

**Cards
of spades and clubs are black in color. Cards
of hearts and diamonds are red in colur**

**(ii)
In 13 cards of each suit, there are three honour cards, or face cards namely
kings, Queens, and Jocker (or Knaves).**

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