Probability of Two Marbles Drawn: Black & Diff Cols

[kenny1999]

Homework Statement

A bag contains 3 black marbles, 2 green marbles and 1 white marble. Two marbles are drawn at random from the bag WITH replacement. Find the probabilities that the two marbles are

(a)black
(b)of different colours

Homework Equations

The Attempt at a Solution

(a)P(both black) = 3/6 x 3/6 = 1/4

(b) I have two attempts for this.

Attempt A
P(of different colours) = P(B,G) + P(B,W) + P(G,W) + P(G,B) + P(W,B) + P(W,G)
= (3/6)(2/6) + (3/6)(1/6) + (2/6)(1/6) + (2/6)(3/6) + (1/6)(3/6) + (1/6)(2/6)
= 22/36

Attempt B
P(of different colours) = 1 - P(both black) - P(both green) - P(both white)
= 1 - (3/6)(3/6) - (2/6)(2/6) - (1/6)(1/6)
= 22/36

Any problems for any of the attempt above?

 

[tiny-tim]

hi kenny1999!

looks fine

(B is probably neater than A)

 

[kenny1999]

hi kenny1999!

looks fine

(B is probably neater than A)

but are they both correct?

 

[tiny-tim]

yes of course!

(didn't i say so? )