પેટી A માં છ લાલ અને ચાર કાળા દડા છે અને પેટી | vedclass

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Question

(a) Let the events are

${R_1} = A$ red ball is drawn from urn $A$ and placed in $B$

${B_1} = A$ black ball is drawn from urn $A$ and placed in $

Vedclass · Accepted Answer

$\frac{{32}}{{55}}$

Vedclass · Answer

(a) Let the events are

${R_1} = A$ red ball is drawn from urn $A$ and placed in $B$

${B_1} = A$ black ball is drawn from urn $A$ and placed in $B$

${R_2} = A$ red ball is drawn from urn $B$ and placed in $A$

${B_2} = A$ black ball is drawn from urn $B$ and placed in $A$

$R = A$ red ball is drawn in the second attempt from $A$

Then the required probability

$ = P({R_1}{R_2}R) + ({R_1}{B_2}R) + P({B_1}{R_2}R) + P({B_1}{B_2}R)$

$ = P({R_1})P({R_2})P(R) + P({R_1})P({B_2})P(R) + P({B_1})P({R_2})P(R) + $

$P({B_1})P({B_2})P(R)$

$ = \frac{6}{{10}} 	imes \frac{5}{{11}} 	imes \frac{6}{{10}} + \frac{6}{{10}} 	imes \frac{6}{{11}} 	imes \frac{5}{{10}} + \frac{4}{{10}} 	imes \frac{4}{{11}} 	imes \frac{7}{{10}} + \frac{4}{{10}} 	imes \frac{7}{{11}} 	imes \frac{6}{{10}}$

$ = \frac{{32}}{{55}}$.

Similar Questions

ધારો કે ઘટનાઓ $A$ અને $B $ માટે, $P\left( {\overline {A \cup B} } \right) = \frac{1}{6}\;,P\left( {A \cap B} \right) = \frac{1}{4}$ અને $P\left( {\bar A} \right) = \frac{1}{4}$ છે,તો ઘટનાઓ $A$ અને $B$. . . . . .