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insens350 [35]
2 years ago
10

g An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single b

all is drawn from each urn. The probability that both balls are the same color is 0.44. Calculate the number of blue balls in the second urn.
Mathematics
1 answer:
Fed [463]2 years ago
5 0

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 P(R_1)=\frac{\textrm {Number of red ball}}{\textrm {Total ball}}    =\frac{4}{10}

Getting a blue ball from first urn is P(B_1)=\frac{\textrm {Number of blue ball}}{\textrm {Total ball}} =\frac {6}{10}

Getting a red ball from second urn is P(R_2)=\frac{\textrm {Number of red ball}}{\textrm {Total ball}}    =\frac{16}{16+x}

Getting a blue ball from second urn is P(B_2)=\frac{\textrm {Number of blue ball}}{\textrm {Total ball}} =\frac {x}{16+x}

Getting two red balls from first and second urn is =\frac{4}{10}\times \frac{16}{16+x}

                                                                                  =\frac{32}{5(16+x)}

Getting two blue balls from first and second urn is =\frac{6}{10}\times \frac{x}{16+x}

                                                                                  =\frac{3x}{5(16+x)}

The probability that both balls are the same in color is =\frac{32}{5(16+x)}+\frac{3x}{5(16+x)}

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

\Rightarrow \frac{32+3x}{5(16+x)} =0.44

\Rightarrow \frac {32+3x}{(80+5x)} =0.44

\Rightarrow 32+3x =0.44(80+5x)

\Rightarrow 32+3x =35.2 +2.2x

\Rightarrow 3x -2.2 x= 35.2 -32

\Rightarrow 0.8x= 3.2

\Rightarrow x = 4

Therefore the of blue in the second urn is 4.

               

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