First fuse works, will the second one work too?

Question

A box contains 8 fuses: 6 are good and 2 are blown. You pull two fuses one after another without replacing the first. The first fuse you test is good. Given that, what is the probability the second fuse is also good?

Accepted Answer

After removing one good fuse, the box holds: - 8 - 1 = 7 fuses total, - 6 - 1 = 5 good fuses. Each remaining fuse is equally likely to be next, so: P(	ext{second good} \mid 	ext{first good}) = \frac{5}{7} \approx 0.714. Taking out a good fuse leaves proportionally fewer good ones, nudging the chance down from the starting 6/8 = 3/4 to 5/7. Takeaway. Without replacement the composition of the box changes after each draw, so recompute the good-to-total ratio on the updated box.

First fuse works, will the second one work too?

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