A jar contains four red marbles and six green marbles. You randomly select a marble from the jar, with replacement. The random variable represents the number of red marbles. What is the probability of getting exactly two red marbles out of four trials?

The probability of getting exactly two read marbles is P = 0,003456%

Step-by-step explanation:

So, each of the following sequences are the desired results (I will use R for a red marble and G for a green marble).

S (1) = R-R-G-G

S (2) = R-G-R-G

S (3) = R-G-G-R

S (4) = G-R-R-G

S (5) = G-R-G-R

S (6) = G-G-R-R

In all, considering there are replacement, there can be 10*10*10*10 = 10000 total sequences, so the probability of getting exactly two read marbles is

P = / frac{P (S (1)) + P (S (2)) + P (S (3)) + P (S (4)) + P (S (5)) + P (S (6)) }{10000}

where

P (S (1)) = P (S (2)) = P (S (3)) = P (S (4)) = P (S (5)) = P (S (6)) = (0.4) ^{2} * (0.6) ^{2} = 0.16*0.36 = 0.0576.

The probability of getting exactly two read marbles is

P = / frac{6*0.0576}{10000} = 0,003456%