Question 856132
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Hi,
FOOD for THOUGHT...
Yep...It is  1/162 = 8/1296, taking into consider the different order of getting the white ball,{{{4*8/1296}}}
60 balls: 10 white(1/6), 20 black(1/3) and 30 red balls(1/2).
4 balls chosen with repositioning: Assume that means with replacement
that is: 1/6 are white and 5/6 are NOT white in reference to i)
P(chose at least one white ball = 1 - P(no white) 
                                = {{{1- (5/6)(5/6)(5/6)(5/6) = 1-(5/6)^4}}} = .5177
ii) P(chose at least one white ball|no red) 
P(choosing only white and/or black with at least one white ball)
P(1 W) = (1/6)(1/3)(1/3)(1/3) = {{{1/162 = 8/1296}}} (4 different orders)
2 W = (1/6)(1/6)(1/3)(1/3) =  1/324 = 4/1296   (6 different orders)
3 W =  (1/6)(1/6)(1/6)(1/3) =  1/648 = 2/1296  (4 orders)
4 W =  (1/6)(1/6)(1/6)(1/6) =  1/1296 (1 way)
P = {{{green(4(8/1296)) + 6( 4/1296) + 4(2/1296) + 1/1296 = 65/1296}}} = .0502
iii) P(no red|chose at least one white ball) 
see ii) P choosing only white and/or black balls with at least one white