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ધારો કે $A$ અને $B$ બે નિરપેક્ષ ઘટનાઓ છે. $P(A)\,\, = \,\,\frac{1}{5},\,\,P(A\,\, \cup \,\,B)\,\, = \,\,\frac{7}{{10}}\,$ હોય તો $P(\overline B )$ બરાબર શું થાય ?
$3/8$
$2/7$
$7/9$
આપેલ પૈકી એક પણ નહિં
Solution
ધારો કે $P(\overline B )\,\, = \,\,x\,.$ હોય, તો$P(B)\,\, = \,\,1\,\, – \,\,x.$
$\therefore \,\,P(A\,\, \cap \,\,B)\,\, = \,\,P(A)\,P(B)\,\, = \,\,\frac{1}{5}\,(1\,\, – \,\,x)$
પરંતુ$P(A\,\, \cup \,\,B)\,\, = \,\,P(A)\,\, + \,\,P(B)\,\, – \,\,P(A\,\, \cap \,\,B)\,\,\,$
$ \Rightarrow \,\,\frac{7}{{10}}\,\, = \,\,\frac{1}{5}\,\, + \,\,(1\, – \,x)\, – \,\frac{1}{5}\,(1\, – \,x)$
અથવા $\frac{1}{2}\,\, = \,\frac{4}{5}\,(1\, – \,x)\,$
$\therefore \,\,\,\,\,1\,\, – \,\,x\,\, = \,\,\frac{5}{8}\,\,\,\,$
$\,\therefore \,\,\,\,x\,\, = \,\,\frac{3}{8}\,.$
