Correct Answer - Option 2 :
\(\frac34\)
Concept:
In a random experiment, let S be the sample space and let E ⊆ S .Then, E is an event.
The probability of occurrence of E is defined as, \(\rm P(E)=\frac{n(E)}{n(S)}\), where, n(E) = number of elements in E and n(S) = number of possible outcomes.
P(Getting E) = 1 - P(Not getting E) OR P(Event happenning ) = 1 - P(Event not happenning)
Calculation:
Total number of balls = (6 + 8 + 10) = 24.
Let S be the sample space. Then, n(S) = 24
Let E be the event of drawing a red ball. Then, n(E) = 6
P(getting a red ball) = \(\rm P(E)=\frac{n(E)}{n(S)}\)
\(=\frac{6}{24}=\frac{1}{4}\)
Now, probability of not getting red ball = 1 - P(getting a red ball)
\(= \rm 1-\frac{1}{4}\\ =\frac{3}{4}\)
Hence, option (2) is correct.