If P(A)=3|5, n(A)=24 then n(S) =? *
Answers
SOLUTION
GIVEN
n(A) = 24
TO DETERMINE
The value of n(S)
CONCEPT TO BE IMPLEMENTED
PROBABILITY OF AN EVENT
In any random experiment if the total number of elementary ( simple) events in the sample space be n ( a finite number) among which the number of elementary events favourable to an event E , connected with the experiment be m then the probability of the event E is denoted by P (E) and defined as
EVALUATION
Here it is given that
n(A) = 24
With usual notations
S = Sample space for the given experiment
n(S) = The total number of possible outcomes
n(A) = Total number of possible outcomes for the event A
So by the definition of probability
FINAL ANSWER
The required value is n(S) = 40
━━━━━━━━━━━━━━━━
Learn more from Brainly :-
1. If E is any event of a random experiment then the probability of the event E belongs to
https://brainly.in/question/28873831
2. Find probability of a 10 year flood occurring at least once in the next 5 years
https://brainly.in/question/23287014
Answer:
SOLUTION
GIVEN
\displaystyle \sf{P(A) = \frac{3}{5} }P(A)=
5
3
n(A) = 24
TO DETERMINE
The value of n(S)
CONCEPT TO BE IMPLEMENTED
PROBABILITY OF AN EVENT
In any random experiment if the total number of elementary ( simple) events in the sample space be n ( a finite number) among which the number of elementary events favourable to an event E , connected with the experiment be m then the probability of the event E is denoted by P (E) and defined as
\displaystyle \sf{}P(E) = \frac{m}{n}P(E)=
n
m
EVALUATION
Here it is given that
\displaystyle \sf{P(A) = \frac{3}{5} }P(A)=
5
3
n(A) = 24
With usual notations
S = Sample space for the given experiment
n(S) = The total number of possible outcomes
n(A) = Total number of possible outcomes for the event A
So by the definition of probability
\displaystyle \sf{P(A) = \frac{n(A)}{n(S)} }P(A)=
n(S)
n(A)
\implies\displaystyle \sf{ \frac{3}{5} = \frac{24}{n(S)} }⟹
5
3
=
n(S)
24
\implies\displaystyle \sf{ n(S) = \frac{24}{\frac{3}{5}} }⟹n(S)=
5
3
24
\implies\displaystyle \sf{ n(S) = 24 \times \frac{5}{3} }⟹n(S)=24×
3
5
\implies\displaystyle \sf{ n(S) = 8 \times 5}⟹n(S)=8×5
\implies\displaystyle \sf{ n(S) = 40 }⟹n(S)=40
FINAL ANSWER
The required value is n(S) = 40