Question

A bin contains 71 light bulbs of which 9 are defective. If 6 light bulbs are randomly selected from the bin with replacement, how do you find the probability that all the bulbs selected are good ones?

Answer 1

`(62/71)^6` But to avoid the curse of the lazy-monster, you must earn the treasure hidden in the cave (the answer fully simplified)... by reading the explanation.

Explanation:

If 9 of the 71 bulbs are defective, then 62 are good. That gives you a `62/71` chance of getting a good one once. You said that they were replaced, so that means that each time you get a bulb, it is independent from the previous draws, because taking a bulb out and putting it back in doesn't affect the ratio of good to defective.

So, the second time you draw, it will still be a `62/71` chance of a good bulb. However, if you find the chances of getting 2 in a row, you'll see that the 2nd draw is a `62/71` chance after getting a `62/71` chance. So, it's actually `62/71` of `62/71`, or `(62/71 * 62/71)`.

Repeat this for 6 times, because you draw six times, and you get `(62/71)^6` which equates to `0.4434` or `44.34` percent.