[tex] |\Omega|=25\cdot24\cdot23=13800\\
|A|=5\cdot4\cdot3=60\\\\
P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\% [/tex]
The probability of an event is calculated as = [tex] \frac{Favorable outcomes}{Total number of outcomes} [/tex]
Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles
So, total marbles = 25 marbles
Number of favorable or green marbles = 5 marbles
Probability of three green marbles if drawn with replacement = [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] ×[tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] × [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{1}{125} [/tex]
