Answer:
Therefore the of blue in the second urn is 4.
Step-by-step explanation:
Let second urn contain x number of blue ball .
Urn Red Ball Blue Ball Total Ball
1 4 6 10
2 16 x 16+x
Getting a red ball from first urn is
![=\frac{4}{10}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B10%7D)
Getting a blue ball from first urn is
![=\frac {6}{10}](https://tex.z-dn.net/?f=%3D%5Cfrac%20%7B6%7D%7B10%7D)
Getting a red ball from second urn is
![=\frac{16}{16+x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B16%7D%7B16%2Bx%7D)
Getting a blue ball from second urn is
![=\frac {x}{16+x}](https://tex.z-dn.net/?f=%3D%5Cfrac%20%7Bx%7D%7B16%2Bx%7D)
Getting two red balls from first and second urn is ![=\frac{4}{10}\times \frac{16}{16+x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B10%7D%5Ctimes%20%5Cfrac%7B16%7D%7B16%2Bx%7D)
![=\frac{32}{5(16+x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B32%7D%7B5%2816%2Bx%29%7D)
Getting two blue balls from first and second urn is ![=\frac{6}{10}\times \frac{x}{16+x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B6%7D%7B10%7D%5Ctimes%20%5Cfrac%7Bx%7D%7B16%2Bx%7D)
![=\frac{3x}{5(16+x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3x%7D%7B5%2816%2Bx%29%7D)
The probability that both balls are the same in color is ![=\frac{32}{5(16+x)}+\frac{3x}{5(16+x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B32%7D%7B5%2816%2Bx%29%7D%2B%5Cfrac%7B3x%7D%7B5%2816%2Bx%29%7D)
Given that the probability that both balls are the same in color is 0.44.
According to the problem,
![\frac{32}{5(16+x)}+\frac{3x}{5(16+x)}=0.44](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B5%2816%2Bx%29%7D%2B%5Cfrac%7B3x%7D%7B5%2816%2Bx%29%7D%3D0.44)
![\Rightarrow \frac{32+3x}{5(16+x)} =0.44](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B32%2B3x%7D%7B5%2816%2Bx%29%7D%20%3D0.44)
![\Rightarrow \frac {32+3x}{(80+5x)} =0.44](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%20%7B32%2B3x%7D%7B%2880%2B5x%29%7D%20%3D0.44)
![\Rightarrow 32+3x =0.44(80+5x)](https://tex.z-dn.net/?f=%5CRightarrow%2032%2B3x%20%3D0.44%2880%2B5x%29)
![\Rightarrow 32+3x =35.2 +2.2x](https://tex.z-dn.net/?f=%5CRightarrow%2032%2B3x%20%3D35.2%20%2B2.2x)
![\Rightarrow 3x -2.2 x= 35.2 -32](https://tex.z-dn.net/?f=%5CRightarrow%203x%20-2.2%20x%3D%2035.2%20-32)
![\Rightarrow 0.8x= 3.2](https://tex.z-dn.net/?f=%5CRightarrow%200.8x%3D%203.2)
![\Rightarrow x = 4](https://tex.z-dn.net/?f=%5CRightarrow%20x%20%3D%204)
Therefore the of blue in the second urn is 4.