Question 1207265
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Part 1


Let's find the probability of getting 3 red marbles in a row.
7 red out of 7+6+8 = 21 total
7/21 = probability of getting a red marble
6/20 = probability of a second red marble (no replacement)
5/19 = probability of a third red marble (no replacement)
Note the countdown of numerator and denominator. These countdowns are because of the no replacement. 
(7/21)*(6/20)*(5/19) = 1/38 is the probability of selecting 3 red marbles in a row (no replacement)
Another approach is to use the nCr combination formula to find there are 7C3 = 35 ways to pick the 3 red marbles out of 21C3 = 1330 ways to select 3 marbles. Then 35/1330 = 1/38


Now calculate the probability of getting 3 white marbles in a row.
6 white out of 21 total
6/21, 5/20, 4/19 are the probabilities of 1st,2nd,3rd marbles as white if there's no replacement.
(6/21)*(5/20)*(4/19) = 2/133 is the probability of selecting 3 white marbles in a row with no replacement.


Lastly we'll find the probability of getting 3 blue marbles in a row.
8 blue out of 21 total
8/21, 7/20, 6/19 are the probabilities of 1st,2nd,3rd marbles as blue where there's no replacement.
(8/21)*(7/20)*(6/19) = 4/95 is the probability of selecting 3 blue marbles in a row with no replacement.



To summarize so far
P(3 red) = 1/38
P(3 white) = 2/133
P(3 blue) = 4/95
Add up those fractions to get 111/1330 = <font color=red>0.0835</font> as the approximate probability of getting 3 of the same color in a row.
Note that those 3 probability values we added represent mutually exclusive events. 


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Part 2


7 red + 8 blue = 15 red or blue out of 7+6+8 = 21 marbles total
15/21, 14/20, 13/19 are the probability values for 1st,2nd,3rd marbles as non-white if no replacements are made.


Multiply out those fractions to get 13/38 = <font color=red>0.3421</font> approximately.



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Answers:
Probability all three marbles are the same color.
<font color=red>0.0835</font>


Probability that none of the three marbles are white.
<font color=red>0.3421</font>


Both results are approximate.
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