A bag contains five blue marbles, five red marbles, five white marbles, and five black marbles. You draw a marble from the bag, and then draw another marble from the bag.
Do you have a greater probability of drawing two blue marbles if you replace the first marble after you draw it or if you don't replace the marble?
Your answer should include both the mathematical proof and a written statement.
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There are 20 marbles in the bag of which 5 are blue.
Therefore the probability of the first marble being drawn being blue = 5/20.
If you replace the marble there are still 20 marbles in the bag and 5 are blue. Therefore the probability of the second marble also being blue is again 5/20.
As you need both to be blue you MULTIPLY the individual probabilities
5/20 * 5/20 = 25/400 = 1/16
IF You DO NOT replace the marble
The probability of the first marble being blue is still 5/20
However after this is drawn there now remain 19 marbles in the bag and only 4 are blue.
Therefore the probability that the second is blue given that the first is also blue = 4/19
Multiply the individual probabilities together
5/20 * 4/19 = 20/380 = 1/19
As 1/16 > 1/19 you have a greater probability if you REPLACE the first marble
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