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  • A committee of 4 students is selected at random from a group consisting of 7 boys and 4 girls. Find the probablity that there are exactly 2 boys in the committee, given that at least one girl must be there in the committee.   

A committee of 4 students is selected at random from a group consisting of 7 boys and 4 girls. Find the probablity that there are exactly 2 boys in the committee, given that at least one girl must be there in the committee. 

 

 

 

 
 
 
 
 

Answers (1)

Let A : exactly 2 boys are in the committee.

      B : at least one girl must be in the committee.

So, P(B)=\frac{^{4}\textrm{C}_1\times ^{7}\!\textrm{C}_3+^{4}\!\textrm{C}_2\times ^{7}\!\textrm{C}_2+^{4}\!\textrm{C}_3\times ^{7}\!\textrm{C}_1 +^{4}\!\textrm{C}_4\times ^{7}\!\textrm{C}_0}{^{11}\textrm{C}_4}=\frac{59}{66}

\& \; \; \; P(A\cap B)=\frac{^4\!\textrm{C}_2\times ^7\!\textrm{C}_2 }{^{11}\!\textrm{C}_4}=\frac{21}{55}

Now 

P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{21}{55}}{\frac{59}{66}}=\frac{126}{295}

 

Posted by

Ravindra Pindel

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