Menu Close

if-P-A-and-P-B-are-independent-events-then-P-A-B-




Question Number 35915 by Rio Mike last updated on 25/May/18
if P(A) and P(B) are independent  events then P(A∣B)=??
$${if}\:{P}\left({A}\right)\:{and}\:{P}\left({B}\right)\:{are}\:{independent} \\ $$$${events}\:{then}\:{P}\left({A}\mid{B}\right)=?? \\ $$
Answered by $@ty@m last updated on 26/May/18
P(A╱B)=((P(A∩B))/(P(B))) ....(i)  ∵ P(A) and P(B) are independent  ∴P(A∩B)=P(A). P(B) ...(ii)  From (i) and (ii)  P(A╱B)=P(A)
$${P}\left({A}\diagup{B}\right)=\frac{{P}\left({A}\cap{B}\right)}{{P}\left({B}\right)}\:….\left({i}\right) \\ $$$$\because\:{P}\left({A}\right)\:{and}\:{P}\left({B}\right)\:{are}\:{independent} \\ $$$$\therefore{P}\left({A}\cap{B}\right)={P}\left({A}\right).\:{P}\left({B}\right)\:…\left({ii}\right) \\ $$$${From}\:\left({i}\right)\:{and}\:\left({ii}\right) \\ $$$${P}\left({A}\diagup{B}\right)={P}\left({A}\right) \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *