CPhill

(3/4)^x=5      take the log of both sides

log(3/4)^x  = log(5)     and by a log property, we have

x * log(3/4)  = log(5)    divide both sides by log(3/4)

x  = log(5)/log(3/4) = about -5.6

The probability is given by

C(7,2) / C(15,2)  = 1/5 or 20%

Another way to see this is that we have a 7/15 chance on the first draw of getting a red chip and a 6/14 chance on the second draw of getting a red one.

So

7/15  x  6/14  = 

7/14 x 6/15 =

1/2  x 2/5  =

1/5

Here's a "formal" proof that shows that 1 + 1 = 2

154 = pi * r^2      divide both sides by pi

154/pi = r^2        take the positive root of both sides

about 7 cm

Don't worry....I'll be back to my old "grumpy" self in a few days......I've been sick and I'm out of practice......LOL!!!!

.025^3   = 0.000015625

So

(4/3) * pi * 0.000015625  = 

0.0000654498469498 cubic units

Circumference = pi * d    =  pi * 28 = about 88 inches

Since the sum of the probabilites = 1, we have

1 - (1/2) - (1/5) =

10/10  - 5/10  - 2/10 = 

3/10      and that's the probability of landing  in region C

about     0.00000000000000000000001195      { more or less  }