Random Occurrence

Let us see about the experiment of random occurrence,

              An outcome is produced from an operation through experiment is called as random experiment and also produce different possible outcomes. In a random experiment, an outcome random experiment is unpredictable.

Some more examples for random occurrence in random experiment:

• Coin is Tossing
• Die is rolling
• Take a card from a packet of card.
• Take a possible ball from bag contains different balls.

Some definitions about random occurrence:

Let we see about some definitions about random occurrence,

Trial: Random experiment performing by this. 

Sample space: In a random occurrence,the possible outcomes are taken by in set is known as sample space and is represented as S. When we roll a die, the possible outcomes are 1, 2, 3, 4, 5, 6 .
Sample space is S = { 1, 2, 3, 4, 5, 6} 

Event: Possible outcome or combination of outcomes is known as an event.An each subset of the sample space S is known as an event. Events represented as  A, B, C, D, E. While coin is tossing, getting a head or tail is take as an event. S = { H, T}, A = {H}, B = {T}.

Formula for random occurrence:

Let we see about formula for random occurrence,      

If a sample space contains n outcomes, m of which are favorable to an event E, then the probability of an event E, denoted by P (E), 
Number of favorable outcomes
  P(E)  =  Total number of outcomes number of favorable outcomes / Total number of outcomes

           = P(E) / P(S)

here,P(E) - Total number of outcomes number of favorable outcomes.

       P(S) - Total number of outcomes.

Examples:

1) Find the random occurrence (probability) to getting two heads when two coins are tossed simultaneously?

Solution:

In tossing two coins the sample space S = {HH, HT, TH, TT}, n(S) = 4.
Let A denote the event of getting two heads A = {HH}, n(A) = 1.
Therefore,probability to getting two heads P =n(A)/n(S) = 1/4.

2) Find the random occurrence getting 3 when rolling a die?

Solution:

 In rolling a die, the sample space S ={ 1, 2, 3, 4, 5, 6} : n (S) = 6.
 Let A be an event of getting 3
 A = { 3 }, n (A) = 1

∴ P(A)  = n(A) / n(S)

= 1/ 6.