Question

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?

Answer 1

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

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%