Next draw red after a mixed removal

Question

A jar holds 8 red marbles and 8 green marbles, 16 in total. So far 2 red marbles and 1 green marble have been drawn and set aside. You now draw one more marble.

Given those three marbles already removed, what is the probability the next draw is red?

Accepted Answer

The condition resets the jar to its current contents. After removing 2 red and 1 green, what remains is 6	ext{ red}+7	ext{ green}=13	ext{ marbles}. The chance the next draw is red is the red fraction of the current jar: P(	ext{next red})=\frac{6}{13}\approx 0.462. Notice it dropped just below one-half, because two reds left but only one green did, tilting the jar slightly green. Takeaway. Track exactly how many of each color departed. Here removing more reds than greens pushed the next-red chance below the original even split.

Next draw red after a mixed removal

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