Proof the the equation in the black writint using the equation in blue writing ectio P(AUB)...

Question

Question

Proof the the equation in the black writint using the equation in blue writing
ectio P(AUB) P(A)+P(B)-P(Ane). AUB P(AUB) P(A) +P(B) AAR

Answer 1

Answer #1

If we express the event $AUB$ as the union of two exclusive events $A$ and $A^{^{c}}cap B$ .As is clear from the figure.

ADB Anß

$AUB$ = $A cup (A^{c ca ca} cap B)$

Since the events on right hand side are exclusive, by axiom. 3 (i.e. P( $AUB$ ) = P(A) + P(B) if A and B are mutually exclusive events)

$P(A cup B) = P(A) + P ( A^{c} cap B)$ ----------(1)

We know that,

$P ( A^{c} cap B) = P (B) - P( A cap B)$ ------------(2)

Putting the value of $P ( A^{c} cap B)$ from (2) in (1), we get

$P(A U B) = P(A) + P(B) _ P(Αλ B )$

Answer 2

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