Question

let a and b be two given independent events such that p(a)=p and p(b)=q and p (exactly one of A, B) then the value of 3p+3q-6pq isplease anyone​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

Two events A & B are said to be independent if

$\sf{ \: P(A \cap B) = P(A) P(B)\: }$

GIVEN

let A and B be two given independent events such that P (A )=p and P (B )=q

TO DETERMINE

Express 3p+3q-6pq in terms of P(Exactly one of A, B)

CALCULATION

Since Two events A & B are said to be independent

So

$\sf{ \: P(A \cap B) = P(A) P(B)\: }$

$\implies \: \sf{ \: P(A \cap B) = pq\: }$

Now the event exactly one of A and B is

$\sf{A \bar{ B}\: \cup \: \bar{A}B}$

So

$\sf{P( \sf{A \bar{ B}\: \cup \: \bar{A}B} )}$

$= \sf{P(A )P(\bar{ B})\: + \: P(\bar{A}) \: P(B)}$

$= \sf{P(A )(1 - P({ B}))\: + \: (1 - P({A})) \: P(B)}$

$= \sf{P(A ) - P(A )P({ B})\: + \: P(B) - P({A}) \: P(B)}$

$= \sf{P(A ) + \: P(B) - 2P({A}) \: P(B)}$

$= \sf{ p + q - 2pq\: } \:$

Hence

$\sf{3 p + 3q - 6pq\: } \:$

$= 3(\sf{ p + q - 2pq\: } )$

$= 3 \: \sf{P( \sf{A \bar{ B}\: \cup \: \bar{A}B} )}$

$= 3 \times \sf{P(Exactly \: one \: of \: A, B)}$

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Answer 2

Answer:

Step-by-step explanation: