The <em>correct answer</em> is:
144/2197
Explanation:
Drawing the balls with replacement means that the events are independent. This means to find the probability of all 3 balls being drawn, we multiply.
The probability of drawing a yellow ball is 9/13, since there are 9 yellow balls out of 13 total.
The probability of drawing the first purple ball is 4/13, since there are 4 purple balls out of 13 total.
The probability of drawing the second purple ball is 4/13, since there are still 4 purple balls out of 13 total.
This gives us:
(9/13)(4/13)(4/13) = (9*4*4)/(13*13*13) = 144/2197.
