There are 2 green marbles, 3 red marbles, and 4 blue marbles in a bag. You will draw one, replace it and draw another.?

Let's break this up into pieces.

Let's look at the green first.

The probability of drawing green is 2/9.
With replacement, the probability of drawing a green again is 2/9.

So the probability of both happening is the product of the individual probabilities, or:

(2/9)² = 4/81

Now let's look at the reds. Similar logic just slightly different numbers:

(3/9)² = 9/81 (didn't reduce here since we'll be adding fractions later so need the common denominator).

And finally the blues:

(4/9)² = 16/81

Now if we add them up we get the probability of both green OR both red OR both blue (aka, both the same color):

4/81 + 9/81 + 16/81 = 29/81 or approx 0.358 (rounded to 3DP)...Show more

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