Question

identifying an error
francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. he has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. explain the error in his solution.
(\frac{2}{12})(\frac{4}{12}) = \frac{8}{144}

Explanation:

Step1: Calculate total marbles initially

The total number of marbles initially is $3 + 2+4 + 3=12$.

Step2: Analyze first - draw probability

The probability of drawing a yellow marble first is $\frac{2}{12}$ since there are 2 yellow marbles out of 12 total marbles.

Step3: Analyze second - draw probability

After drawing a yellow marble and not replacing it, there are now $12 - 1 = 11$ marbles left. The probability of then drawing a red marble is $\frac{4}{11}$, not $\frac{4}{12}$.

Step4: Identify error

Francisco used 12 as the denominator for the second - draw probability instead of 11, which is incorrect for non - replacement situation.

Answer:

Francisco used 12 as the denominator for the probability of drawing a red marble on the second draw instead of 11. Since the first yellow marble was not replaced, there are only 11 marbles left for the second draw, so the correct probability of drawing a red marble after a non - replaced yellow marble is $\frac{4}{11}$, not $\frac{4}{12}$.