Question

A bag contains 3 red and 3 green balls. Write the sample space (S) and n(S) for the experiment of ‘drawing two balls at random simultaneously from the bag’.

Answer 1

Hint: Probability means possibility. It is a branch of mathematics that deals with the occurrence of events. It is used to predict how likely events are to happen. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.
Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
Random experiment is an experiment where we know the set of all possible outcomes but find it impossible to predict one at any particular execution.
Sample space is defined as the set of all possible outcomes of a random experiment. Example: Tossing a head, Sample Space(S) = {H, T}. The probability of all the events in a sample space adds up to 1.
Event is a subset of the sample space i.e. a set of outcomes of the random experiment.
\[{\text{Probability of an event}} = \dfrac{{{\text{Number of occurence of event A in S}}}}{{{\text{Total number of cases in S}}}}{\text{ }}\]
\[ = \dfrac{{n\left( A \right)}}{{n\left( S \right)}}\]

Complete step-by-step answer:
Number of drawing of green balls = n(G) = 3
Number of drawing of red balls = n(R) = 3
Let red balls be R1, R2, R3
Let green balls be G1, G2, G3
Sample space (S) = (R1, R2, R3, G1, G2, G3)
n(S) = 6

Note: There are some main rules associated with basic probability:
For any event A, 0≤P(A)≤1.
The sum of the probabilities of all possible outcomes is 1.
P(not A)=1-P(A)
P(A or B)=P(event A occurs or event B occurs or both occur)
P(A and B)=P(both event A and event B occurs)
The general Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)