Abag contains red balls and white balls. if five balls are to be pulled from the bag, with replacement, the probability of getting exactly three red balls is 32 times the probability of getting exactly one red ball. what percent of the balls originally in the bag are red?

Percentage of balls which are red = 80%.

Step-by-step explanation:

Let the probability of drawing a red ball  be x then the probability of drawing a white ball is 1-x.

There are 5C3 = 10 ways of getting 3 reds in 5 draws so  the probability of this is 10* x^3 * (1 - x)^2.

The probability of getting 1 red in 5 draws = 5C1 * x (1-x)^4.

The  first probability is 32 times the last.

So we have the equation:

10x^3(1 - x)^2  /  5x(1 - x)^4  = 32

2x^2 / (1 - x)^2 = 32

2x^2 = 32(1 -x)^2

2x^2 = 32( 1 - 2x + x^2)

2x^2 = 32 - 64x + 32x^2

30x^2 - 64x  + 32 = 0

15x^2 - 32x + 16 = 0

(5x - 4)(3x - 4) = 0

x = 0.8, 1.333...

The probability must be < 1 so x = 0.8  = 80%.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

600,000,000,000, or 6e14

step-by-step explanation: