# CLASS-10PROBABILITY 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).