A bag contains eight green marbles and four blue marbles.

Question

A bag contains eight green marbles and four blue marbles. Taylor draws two marbles in succession without replacing them in the bag. What is the probability of drawing a green marble on the second draw?

Answer 1

You have an 8/12 = 2/3 chance of picking a green marble the first time and a 4/12 = 1/3 chance of not picking green the first time.

 

If you picked green the first time, you have one less marble AND it's green, so you have a 7/11 chance of picking green again.

 

If you didn't pick green the first time, you still have one less marble to choose from but still as many greens, so you have a 4/11 chance of not picking green the 2nd time.

 

(2/3)(7/11) + (1/3)(4/11) = 14/33 + 4/33 = 18/33

Answer 2

Prob(first is blue and 2nd is green) + Prob( 1st is green and 2nd is green)

 

 4/12*8/11 + 8/12*7/11

 

1/3 * 8/11 + 2/3*7/11

 

= 8/33 + 14/33

 

= 22/33

 

= 2/3