SOLUTION: A bowl contains 4 yellow marbles and 3 red marbles. Michael randomly draws 4 marbles from the bowl. He replaces each marble after it is drawn. What is the probability that he draws

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Question 969845: A bowl contains 4 yellow marbles and 3 red marbles. Michael randomly draws 4 marbles from the bowl. He replaces each marble after it is drawn. What is the probability that he draws 3 yellow marbles and 1 red marble?
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A bowl contains 4 yellow marbles and 3 red marbles. Michael randomly draws 4 marbles from the bowl. He replaces each marble after it is drawn. What is the probability that he draws 3 yellow marbles and 1 red marble?
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Ans: (4/7)^3*(3/7) = 192/2401
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Cheers,
Stan H.
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Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Sampling with replacement. These are independent, and we multiply the probabilities of each to get the joint probability.
Probability of drawing 3 yellow marbles and one red marble is (4/7)*(4/7)*(4/7)*(3/7) * 4. We need the four, because there are four ways this can occur, with the red coming first, second, third, or fourth. Order of appearance of the red marble does not matter. If it did, then the probability would be less.
(192/2401)*4=768/2401
P=0.320.