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.

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Question:  

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.

The Probability is (2/12)(4/12) = 8/144

P = (2/12)(4/11) = 2/33

Step-by-step explanation:

There are total 3 + 2 + 4 + 3 = 12 marbles

The probability of drawing a yellow marble is given by

P(yellow) = number of yellow marbles/total number of marbles

There are 2 yellow marbles and total 12 marbles

P(yellow) = 2/12

Then Francisco draws a red marble without replacing the first one so that means there are total 11 marbles left.

P(red) = number of red marbles/total number of marbles

There are 4 red marbles and total 11 marbles

P(red) = 4/11

Therefore, the overall probability is

P = (2/12)(4/11) = 2/33

Francisco made the error of calculating the probability with replacement whereas, in reality he did not replaced the marble after drawing the yellow marble, so he should have used total 11 marbles for the calculation of drawing red marble,