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?

1 Answer
Ian J.
Mar 7, 2016

(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.

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