SOLUTION: A bin contains 25 lightbulbs, 5 of which are in good condition and will function for at least 30 days, 10 of which are partially defective and will fail in their second day of use,

Question 467118: A bin contains 25 lightbulbs, 5 of which are in good condition and will function for at least 30 days, 10 of which are partially defective and will fail in their second day of use, 10 will not light up. Given that a randomly chosen bulb initially lights, what is the probability it will still be working after one week?
i am still confused how to solve this problem.
IF THE ASKED THE PROBABILITY THAT THE CHOSEN BULB WILL LIGHT AFTER ONE WEEK, THE SOLUTION WOULD BE SIMPLY 5/25 = 1/5.
BUT THE PROBLEM SAYS:::: GIVEN THAT RANDOMLY CHOSEN BULB INITIALLY LIGHTS, WHAT IS THE PROBABILITY THAT THE IT WILL LIGHT AFTER ONE WEEK. This makes me confuse, it looks like that the solution is 5/15 because the bulb was initially lighting and we have 15 bulbs that would light initially.
What is the correct solution? Thanks in advance
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!

Given that a randomly chosen bulb initially lights, it means it is not in 10 that
will not light up.
it is either good or partially defective.

probability that it will still be working after one week (i.e it is good) = 5/15
= 1/3

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