Question

Thomas has a box with four black color bottles and eight gray color bottles. Two bottles are drawn without replacement from the box. What is the probability that both of the bottles are gray

Answer 1

So 4 black and 8 grey. 4+8=12

12 Total bottles

if he takes 2 bottles out of the box, there is a 2/8 chance that he will get both grey ones, because when you have 8 total grey bottles, and you're pulling 2 out, then you have 2 in 8 chance of getting a grey bottle.

Answer 2

-- There are 12 total bottles in the box.  8 of them are grey.

-- The probability of getting a grey bottle on the first draw is  8/12 .

-- Now there are 11 bottles left in the box, and 7 of them are grey

-- The probability of getting a grey bottle on the second draw is  7/11 .

-- The probability of both events happening is

          (8/12) · (7/11) = 56/132  =  14/33  =  about  42.4%  (rounded)