Discussion
There are 2 pots. One pot has 5 red and 3 green marbles. Other has 4 red and 2 green marbles. What is the probability of drawing a red marble?
Answer: B
A pot is chosen first, each with probability \( \tfrac{1}{2} \), and then a marble from it.
\[ P = \frac{1}{2} \times \frac{5}{8} + \frac{1}{2} \times \frac{4}{6} \]
\[ = \frac{5}{16} + \frac{1}{3} = \frac{15}{48} + \frac{16}{48} = \frac{31}{48} \]
Pooling all 14 marbles into one pot would give \( \tfrac{9}{14} \) - the first option - but that would treat the two pots as equally stocked, which they are not.
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