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 ball 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.

The number of blue balls in the second urn is 4.

Given to us:

In Urn 1,

Number of Red balls ,

Number of Blue balls ,

Total Number of balls ,

In Urn 2,

Number of Red balls ,

Number of Blue balls ,

Total Number of balls ,

The probability that both balls are of the same color = 0.44,

Case I: If both the balls are red, then

The probability that the red ball is taken out from urn 1

The probability that the red ball is taken out from urn 2

Therefore, the probability that the red ball is taken out from both the urn is

.

Balls should be red from both the urn, both tasks are to be done together. hence, both the probabilities are multiplied.

Case II: If both the balls are blue, then

The probability that the blue ball is taken out from urn 1

The probability that the blue ball is taken out from urn 2

Therefore, the probability that the blue ball is taken out from both the urn is

.

Balls should be blue from both the urn, both tasks are to be done together. hence, both the probabilities are multiplied.

The probability that both balls are of the same color = 0.44.

As both cases are independent, the probability of both cases is added.

Hence, the number of blue balls in the second urn is 4.

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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    

Getting a blue ball from first urn is

Getting a red ball from second urn is    

Getting a blue ball from second urn is

Getting two red balls from first and second urn is

Getting two blue balls from first and second urn is

The probability that both balls are the same in color is

Given that the probability that both balls are the same in color is 0.44.

According to the problem,

Therefore the of blue in the second urn is 4.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}