SOLUTION: We choose 4 balls with repositioning from a box that contains 10 white, 20 black and 30 red balls. i) What is the probability that we chose at least one white ball? ii)

 

Hi,

FOOD for THOUGHT...

Yep...It is  1/162 = 8/1296, taking into consider the different order of getting the white ball,

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) 

                                =  = .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) =  (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 =  = .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