#1.
There are 8 possible outcomes when we flip a coin three times. (2*2*2 for 2 outcome possibilities on each flip)
We want 2 heads in a row -
So we can have one of three scenarios that work:
1. no tails at all (HHH)
2. Tails in first flip (THH)
3. Tails in third flip (HHT)

So our answer is 3/8.

#2.
This one is like the last one except that we add one more scenario:
4. Tails as second flip (HTH)
So we have 4 outcomes out of 8 total that fit our criteria, or 4/8 as answer.

#3.

We want two threes in a row (probability of each is 1/6)
followed by a different number (probability of this is 5/6)
So we have:
1/6 * 1/6 * 5/6 or 5/216.

The other way to look at this one is this:
There are 216 possible outcomes (6 sides possible each roll, and three rolls, so 6*6*6 = 216.)
The outcomes we like are:
331
332
334
335
336
There are 5 of these, so 5/216 is our answer.


#4.
There are 6*6*6 = 216 possible outcomes.

There are 3 general ways to exactly 2 6's:
66x
6x6
x66

where x = one of the other numbers: 1,2,3,4, or 5
there are 5 ways to get each of the above for example: 661, 662, 663, 664, 665
there are 5 * 3 = 15 ways to get exactly 2 sixes

so, the probability is 15/216

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