1. The chance to draw a red marble on the first trial is 5/20. ··· (1)
2. The chances to draw a red marble in two trials are:
(i). Chance the first trial draws a red, then the second trial draws a red: (5/20){(5-1)/(20-1)}
(ii). Chance the first trial draws a red, then the second trial fails a red: (5/20){(20-5)/(20-1)}
(iii). Chance the first trial fails a red, then the second trial draws a red: {(20-5)/20}{5/(20-1)}
Thus, the chance to draw at least one red in two trials is: (i)+(ii)+(iii) That is:
(5/20){(5-1)/(20-1)} + (5/20){(20-5)/(20-1)} + {(20-5)/20}{5/(20-1)}
={5(5-1)+5(20-5)+5(20-5)} / 20(20-1)=(20+75+75) / 20x19 = 170/380 = 17/38 ··· (2)
CK: Chance each trial fails to draw a red: {(15-1)/20}{(20-5)/(20-1)}=210/380=21/38 ··· (3)
So, (2)+(3)=(17/38)+(21/38)=38/38=1 CKD.
The answer: The probability of at least one being red is 17/38. (=approx.44.7%).