There are 9 yellow and 4 purple balls in a bag. if you randomly choose balls one at a time, with replacement, what is the probability of choosing 1 yellow ball and then 2 purple balls? question 5 options: 165/5210 24/1329 144/2197 28/1335

The correct answer 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.