Answer to Question #204393 in Statistics and Probability for Tyler

Question

A bag of marbles contains 12 red marbles and 16 green marbles. Two marbles are drawn.

What is the probability that:

a) Both marbles are green if the first marble is replaced? (A:2)

b) Both marbles are red if the first marble is not replaced? (A:2)

Answer 1

a) If the first marble is replaced, then the events are independent

$$P(G\ and\ G)=\dfrac{16}{12+16}(\dfrac{16}{12+16})=\dfrac{16}{49}$$

b) If the first marble is not replaced, then the events are dependent

$$P(R\ and\ R)=\dfrac{12}{12+16}(\dfrac{12-1}{12+16-1})=\dfrac{11}{63}$$