Question

If P(A): P(not A)=5:3, then P(A)= _____​

Answer 1

GIVEN :-

• P( A ) : P( Ā ) = 5 : 3

TO FIND :-

• Value of P( A )

SOLUTION :-

ACCORDING TO THE QUESTION :-

$\implies \rm { \: p(a) : p( \bar{a} \: ) = 5 \: : \: 3}$

$\implies \rm { \: \dfrac{ p(a) }{p( \bar{a})} \: = \dfrac{5}{3} }$

$\implies \boxed{ \rm { \: p(a) + p( \bar{a}) } \: = 1 }$

$\implies \boxed{ \rm { \: p( \bar{a}) } \: = 1 \: - p(a)}$

SO PUT THE VALUE OF P( Ā )

$\implies \rm { \: \dfrac{ p(a) }{1 - p( {a})} \: = \dfrac{5}{3} }$

NOW AFTER RECIPROCAL OF THE EQUATION

$\implies \rm { \: \dfrac{1 - p( {a})} { p(a) } = \dfrac{3}{5} }$

$\implies \rm { \: \dfrac{1 }{p(a)} \: - \: \dfrac{p( {a})} { p(a) } = \dfrac{3}{5} }$

$\implies \rm { \: \dfrac{1 }{p(a)} \: - \: 1 = \dfrac{3}{5} }$

$\implies \rm { \: \dfrac{1 }{p(a)} \: = \dfrac{3}{5} \: + \: 1}$

$\implies \rm { \: \dfrac{1 }{p(a)} \: = \dfrac{3 + 5}{5} \: }$

$\implies \rm { \: \dfrac{1 }{p(a)} \: = \dfrac{8}{5} \: }$

$\implies \boxed{ \boxed {\rm { \: p(a)\: = \dfrac{5}{8} \: }}}$

OTHER INFORMATION :-

Probability: It is the numerical measurement of the degree of certainty.

• Theoretical probability associated with an event E is defined as “If there are ‘n’ elementary events associated with a random experiment and m of these are favourable to the event E then the probability of occurrence of an event is defined by P(E) as the ratio m/n

• If P(E) = 1, then it is called a ‘Certain Event’.

• If P(E) = 0, then it is called an ‘Impossible Event’.

• The probability of an event E is a number P(E) such that: 0 ≤ P(E) ≤ 1

• An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.

• Favourable outcomes are those outcomes in the sample space that are favourable to the occurrence of an event.

Answer 2

Answer:

In Short way or for fast calculation :-

we have P(A) : P(not A) =5:3

then ,

P(A) /P(Not A) = 5/3

then we can write as

P(A) = 5 and P(Not A) =3

5+3=8

Then P(A) =5/8

Hope it's helpful