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An urn contains r red balls and b black balls. Now, match the following lists: |
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Answer» a. `(""^(r)C_(2))/(""^(r+b)C_(2))=1/2(r-1)=(r-b)(r+b-1)` `=2r(r-1)=(r+b)(r+b-1)` `or 2r^(2)-2r=r^(2)+(2b-1)r+b^(2)-1` `or r^(2)-(1+2b)+1-b^(2)=0` `or b^(2)+2br+r-r^(2)-1=0` `or b=(-2r+-sqrt(4r^(2)-4(r-r^(2)-1)))/(2)` `=-r+-sqrt(2r^(2)-r+1)` Since b is integer, POSSIBLE values of r are 3 and 8. b. `""^(4)C_(2)((r)/(r+10))((10)/(r+10))^(2)=3/8` c. `((r)/(r+10))^(2)((10)/(r+10))=1/16impliesr=10` d. Probability of GETTING n red balls in 2n draws in always equal to probability of getting EXACTLY n black blalls in 2 n draws for any value of r and b, HENCE the ratio r/b can be `10,3,8,2.` |
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