Data Management Geometric Distribution Probability

Question

Hi. I am having a lot of trouble doing this question. In a box of 25 shirts at Winners, 4 of them are ripped. When she is really bored at work, Aliyah reaches into the box and grabs one shirt at a time and then immediately puts it back into the box. If she repeats this process, what is the probability she will find the first ripped shirt after 3 attempts? 

I got 0.113

But my friend says it's wrong. How would I go about doing this?

Answer 1

Hi Rahman W.,

Perhaps the disagreement you are having with your friend relates to the interpretation of the question. Does "After 3 attempts" mean, on the 4th attempt? Or does it mean, "upon making the 3rd attempt"? I would incline to the former. That math would be the sequential, independent probability of getting non-ripped shirts, that's (21/25)^3 * (4/25), or 0.0948 . If it's the latter, that's the 0.113 . This shows you, incidentally, the difficulty of writing unambiguous problems!

-- Cheers, -- Mr. d.