There is a bag filled with 3 blue, 4 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 getting 2 blues?

1/6

Step-by-step explanation:

The number of blues expected:2

Total number of marbles: 3+4+5 = 12

out of 12, 2 are expected. This in a fraction is 2/12

Simplify to 1/6

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 1/3

(This is because 4 out of 12 marbles are red and 4/12 reduces to 1/3)

The probability of selecting a red marble the second time is 1/3

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

probability of getting 2 reds = (1/3) ^2=1/9