© There is a bag filled with 5 blue, 6 red and 2 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 getting 2 reds?

7.69%

Step-by-step explanation:

there is 7.69% probability of getting 2 reds

How to get that

We have 6 red out of 5+6+2 = 13 total.

The fraction 6/13 represents the probability of selecting red at random.

Because the marble is replaced, the probability does not change on the next selection.

The probability of getting two reds in a row is (6/13)*(6/13) = 36/169

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4