Question 1190339
<font color=black size=3>
Part A


15 white, 25 total
m = P(1st is white) = 15/25 = 3/5
n = P(2nd is white, given 1st is white) = 14/24 = 7/12
P(2 white in a row) = m*n = (3/5)*(7/12) = 21/60 = 7/20


I subtracted 1 from the numerator and denominator when going from 15/25 to 14/24. This is directly due to the fact we aren't replacing the first marble.


Answer: <font color=red>7/20</font>


================================================================
Part B


P(2 white) + P(at least one black) = 1
P(at least one black) = 1 - P(2 white)
P(at least one black) = 1 - 7/20
P(at least one black) = 20/20 - 7/20
P(at least one black) = 13/20


This works because you either get 2 white in a row, or you get at least one black marble (pick one scenario only). The two events are complementary.


Answer: <font color=red>13/20</font>


================================================================
Part C


m = P(1st is white) = 15/25 = 3/5
n = P(2nd is black, given 1st is white) = 10/24 = 5/12
m*n = P(1st is white, 2nd is black) 
m*n = (3/5)*(5/12)
m*n = 15/60
m*n = 1/4


q = P(1st is black) = 10/25 = 2/5
r = P(2nd is white, given 1st is black) = 15/24 = 5/8
q*r = P(1st is black, 2nd is white)
q*r = (2/5)*(5/8)
q*r = 10/40
q*r = 1/4


P(exactly 1 white) = m*n + q*r
P(exactly 1 white) = 1/4 + 1/4
P(exactly 1 white) = 2/4
P(exactly 1 white) = 1/2


It's a coincidence that we end up with exactly 1/2. 
If the initial black and white counts were other values (say 16 black and 15 white) then the answer wouldn't be 1/2.


Answer: <font color=red>1/2</font>
</font>