Answer:
(a) = 0.072 (b) = 0.045
Step-by-step explanation:
(a). The probability of picking a green marble is 5/12 because there are 5 green marbles and 12 marbles in total. Because we replace the marble, this is the probability for all three times we pick a marble. Now to find the total probability we need to times them together. We multiply because the two probabilities are independent of each other, one probability doesn't depend on another probability.
So the answer for (a) = 5/12 × 5/12 × 5/12 = 125/1728 = 0.072
(b). The probability that a green marble is picked the first time is 5/12, the probability that a green marble is picked the 2nd time is 4/11 because we don't replace the marble now we have one less green marble and one marble less in total. The probability that we pick a green marble the 3rd time is 3/10 again because we don't replace the marble. Again, these probabilities are independent so we multiply them.
So the answer for (b) = 5/12 × 4/11 × 3/10 = 60/1320 = 0.045
