Marbles question that I'm confused on

Question

You randomly select 2 marbles from a mug containing 9 blue marbles, 7 red marbles, and 2 white marbles. How many times greater is the probability of selecting 2 red marbles when you replace the first marble before selecting the second marble than when you do not replace the first marble before selecting the second marble? Round your answer to the nearest thousandth.

Answer 1

select 2 red marbles from a mug containing 9 blue, 7 red and 2 white marbles

the probability of drawing 2 red marbles with replacement is (7/18)(7/18)=49/324

the probability of drawing 2 red marbles without replacement is (7/18)(6/17)=42/306

49/324 is how many times 42/306 ?

(49/324)/(42/306)=

(49/324)(306/42)=

14,994/13,608=

1.1018519=

1.102 times greater

Answer 2

With replacement probability is (2/18)*(1/9) = 1/81

Without replacement the probability is (2/18)*(1/17).

The ratio will be 17/9.