Question 946336
  
Given
A bag containing 7 green, 9 black and 6 yellow marbles for a total of 22 marbles.
Five marbles are picked without replacement.
Find probability of all five are of the same colour.
  
Solution
Randomly picked five marbles without replacement out of 22.
There are three possible colours.
P(GGG) = {{{7/22*6/21*5/20 = 1/1254}}}
P(BBB) = {{{9/22*8/21*7/20 = 1/209}}}
P(YYY) = {{{6/22*5/21*4/20*3/19*2/18 = 1/4389}}}
Probability of choosing five marble of any one of the three colours
= P(GGG) + P(BBB) + P(YYY) = {{{1/1254 + 1/209 + 1/4389 = 17/2926 = 0.58%}}}
  
Answer
The probability of randomly choosing 5 marbles of the same colour is approximately 0.58%