There is a bag filled with 4 blue, 3 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of exactly 1 red?

You are selecting marbles with replacement. The marble selections (trials) are independent and the marble selection follows the binomial distribution.

The probability of selecting a red marble the first time is 1313.

(This is because 4 out of 12 marbles are red and412412 reduces to 1313.

The probability of selecting a red marble the second time is 1313.

The marble selections are independent and you can multiply the two probabilities to get the following:

probability of getting 2 reds = (13)2(13)2

=19=19.

So the probability of getting two reds is 1919.

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