The problem involves calculating the probability of selecting defective light bulbs from a set of 25 bulbs, of which 5 are defective, when 8 bulbs are chosen. The focus is on determining the likelihood that 2 or fewer of the selected bulbs are defective.
The discussion is ongoing, with participants exploring different approaches to the problem. Some have provided insights into counting methods and the implications of sampling with or without replacement. There is no explicit consensus on the best method yet.
Participants are navigating the complexities of probability calculations and the assumptions related to sampling methods, particularly the distinction between sampling with and without replacement.
hadroneater said:Homework Statement
Of 25 light bulbs, 5 are defective. 8 bulbs are chosen from the 25. What is the probability that 2 or fewer of the 8 selected light bulbs are defective?
quincyboy7 said:Let's go through some casework.
If no selected light bulbs are defective, there is a (4/5)^8 chance of that happening
If 1 selected light bulb is defective, there is a (4/5)^7*(1/5)*8 chance of that happening.
If 2 selected light bulbs are defective, there is a (4/5)^6*(1/5)^2*8*7 chance of that happening. How I got the integers is by doing 8C8=1, 8C7=8, and 8C6=8*7. This is because order does not matter i.e. if you pick a defective then a good one, it's the same as picking a good one, then a defective.