Question

If A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3P(A) = 2P(B)=P(C), then P(A) is equal to

Answer 1

SOLUTION

GIVEN

A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3P(A) = 2P(B)=P(C),

TO DETERMINE

The value of P(A)

EVALUATION

Here it is given that A, B, C are three mutually exclusive and exhaustive events of an experiment

∴ P(A) + P(B) + P(C) = 1 - - - - - - (1)

Again it is also stated that

3P(A) = 2P(B)=P(C)

Therefore

$\displaystyle \sf{P(C) = 3P(A) \: \: \: and \: \:P(B) = \frac{3P(A)}{2} }$

Equation 1 gives

$\displaystyle \sf{P(A) +\frac{3P(A)}{2} + 3P(A) = 1 }$

$\displaystyle \sf{ \implies \: \frac{11P(A)}{2} = 1 }$

$\displaystyle \sf{ \implies \: P(A)= \frac{2}{11} }$

FINAL ANSWER

$\boxed{ \: \: \displaystyle \sf{ P(A)= \frac{2}{11} \: \: }}$

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