First marble red, is the next one red as well?

Question

A bag holds 5 red and 3 blue marbles, eight in all. You draw two marbles one after another without replacing the first. The first marble is red. Given that, what is the probability the second marble is also red?

Accepted Answer

After removing one red marble, the bag now contains: - 8 - 1 = 7 marbles total, - 5 - 1 = 4 red marbles. Each remaining marble is equally likely to be drawn next, so: P(	ext{second red} \mid 	ext{first red}) = \frac{4}{7} \approx 0.571. Pulling out a red marble makes red slightly scarcer, which is why the chance drops from the original 5/8 down to 4/7. Takeaway. Removing an item of a given color makes that color a bit less likely next time; just re-count the bag after the first draw.

First marble red, is the next one red as well?

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