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Hindi
14.Probability
medium

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 ?

A

$3/8$

B

$2/7$

C

$7/9$

D

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 $\frac{1}{2}\,\, = \,\frac{4}{5}\,(1\, – \,x)\,$

$\therefore \,\,\,\,\,1\,\, – \,\,x\,\, = \,\,\frac{5}{8}\,\,\,\,$

$\,\therefore \,\,\,\,x\,\, = \,\,\frac{3}{8}\,.$

Standard 11
Mathematics

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