How should Della arrange the marbles so she has the best chance of choosing a red marble

Question

the host gives her 2 red marbles, 2 green marbles, and 2 yellow marble. Della will put the marbles into tw indentical cans in any way she choose's. the host will then rearrange the cans, leaving the marbles as Della placed them. Della will then select a can and choose a marble. If she chooses a red marble, she wins

Answer 1

X = green or yellow marble
The probability of selecting the needed can is 1/2

CAN #1        Can #2           Probability of winning

0                  rrXXXX             1/2*1/3 = 1/6 = 16.6666666666...%

X                   rr XXX              1/2*2/5 = 1/5 = 20%

XX                 rr XX                1/2*1/2 = 1/4 = 25%

 

XXX               rr X                  1/2* 2/3 = 1/3 = 33.33333...%

XXXX             rr                     1/2 = 50%

r                   rXXXX                1/2*1 + 1/2*1/5 = 6/10 = 3/5 = 60%

rX                 rXXX                   1/2*1/2 + 1/2*1/4 = 1/4 + 1/8 = 3/8 = 37.5%

rXX               rXX                     1/2*1/3 + 1/2*1/3 = 1/3 = 33.33333....

rXXX             rX                        1/2*1/4 + 1/2*1/2 = 1/8 + 1/4 = 3/8 = 37.5%

rXXXX           r                          1/2*1/5 + 1/2 = 1/10 + 1/2 = 6/10 = 3/5 = 60%

rr                XXXX                       same as 1st case

 

CONCLUSION:

1 can contains a single red marble, other can contains the other 5 marbles.