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.
(StartFraction 2 over 12 EndFraction) (StartFraction 4 over 12 EndFraction) = StartFraction 8 over 144 EndFractionFrancisco 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.
(StartFraction 2 over 12 EndFraction)vFrancisco 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.
(StartFraction 2 over 12 EndFraction) (StartFraction 4 over 12 EndFraction) = StartFraction 8 over 144 EndFraction
Answers
Given : 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. (2/12)(4/12) = 8/144
To find : error in his solution.
Solution:
Green Marbles = 3
Yellow Marbles = 2
Red Marbles = 4
Black Marbles = 3
Total Marbles = 12
Probability of Drawing Yellow Marble = (Yellow Marbles)/ Total Marbles
= 2/12
Francisco has not replaced Yellow Marble Hence
now total Marbles = 12 - 1 = 11
Probability of Drawing Red Marbles = (Red Marbles)/Total Marbles
= 4/11
Probability = (2/12)(4/11) = 8/132 = 2/33
Francisco Solution = (2/12)(4/12) = 8/144
Error in Solution of Francisco that he has considered 12 marbles while drawing reed marbles however now marbles are 11 only as he has not replaced Marble
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Answer:
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