Question

If P(A)=3|5, n(A)=24 then n(S) =? *​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{P(A) = \frac{3}{5} }$

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

$\displaystyle \sf{}P(E) = \frac{m}{n}$

EVALUATION

Here it is given that

$\displaystyle \sf{P(A) = \frac{3}{5} }$

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

$\displaystyle \sf{P(A) = \frac{n(A)}{n(S)} }$

$\implies\displaystyle \sf{ \frac{3}{5} = \frac{24}{n(S)} }$

$\implies\displaystyle \sf{ n(S) = \frac{24}{\frac{3}{5}} }$

$\implies\displaystyle \sf{ n(S) = 24 \times \frac{5}{3} }$

$\implies\displaystyle \sf{ n(S) = 8 \times 5}$

$\implies\displaystyle \sf{ n(S) = 40 }$

FINAL ANSWER

The required value is n(S) = 40

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Answer 2

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