Question

bag has five red marbles, six blue marbles, and four black marbles. What is the probability of picking a red marble, replacing it, and then picking another red marble?

Answer 1

Total marbles in the bag = 15
Red marbles in the bag  =  5

Probability of picking a red marble the first time = 5/15 .
If you put it back, then everything goes back to the beginning.

Probability of picking a red marble the second time = 5/15 .
If you put it back, then everything goes back to the beginning.

Probability of picking a red marble the third time = 5/15 .
If you put it back, then everything goes back to the beginning.

Probability of picking a red marble the fourth time = 5/15 .
If you put it back, then everything goes back to the beginning.
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Probability of picking a red marble the 20th time = 5/15 .
If you put it back, then everything goes back to the beginning.
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Probability of picking a red marble the ' Nth ' time = 5/15 .
If you put it back, then everything goes back to the beginning.


Probability of picking a red marble ' N ' times in a row = (5/15)^N.

Probability of picking a red marble 3 times in a row  = (5/15) (5/15) (5/15).

Probability of picking a red marble 2 times in a row = (5/15) x (5/15)

                                                                       =  (25/225) = 1/9

                                                                       =      11.1%  (rounded).

Answer 2

Add all the marbles together
5 (red) + 6 (blue) + 4 (black) = 15 marbles total
5 / 15 = 1/3
33% chance of picking a red marble
If you replace the red marble with another red marble, it would still be 33% since you're basically just putting the red marble back to re pick it (consecutively).
If you replaced the red marble, it would be 4 /15 since 5 - 1 = 4
4 / 15 = .27
27% of picking a red marble after replacing with a different color