The following are 2 practice questions for my math class. There will be similar questions on my test so I need to know how to do them correctly. Any help would be great, thanks!

1) Following are 3 boxes containing letters: [tex] [AND] [HISTORY].

a) From box 1, three letters are drawn one-by-one without replacement and recorded in that order. What is the probability that the outcome is HAT?

-I did (1/4)(1/3)(1/2) = 1/24 Is this correct?

b) If a box is chosen at random and then a letter is drawn at random from the box, what is the probability that the outcome is A?

-I'm thinking along the lines of (2/3)(1/4)(1/3), but am unsure...

2)Box 1:[2 black balls & 3 white balls]Box 2:[4 black balls & 2 white balls] A ball is drawn at random from box 1, then at random from box 2. The colors of the balls are recorded in order. The boxes look like this:

1:[BBWWW] 2:[BBBBWW] Find:

a) The probability of 2 whites.

-I did (3/5)(2/6) = 1/5 Is this correct?

b) The probability of at least one black. (I'm stumped)

c) The probability of at most one black. (I'm stumped again)

d) The probability of a black followed by a white, or a white followed by a black.

-I did (2/5)(2/6) = 2/15 or (3/5)(4/6) = 2/5 Is this correct?