Classical/theoretical probability

Probability is a number between 0 and 1, inclusive: 0≤P(E)≤1. Don't use percentages or fractions.

A set of equally-likely outcomes, the sample space S.
An event is any subset of S.
The probability of the event is the number of outcomes it has, i.e. the size of the event, divided by the total number of outcomes, i.e. the size of S. P(E)=|E|/|S|

Complement of event A is Ā = S-A. Probability of Ā = 1-P(A) and P(A)=1-P(Ā)

Probability experiment: roll a die

Sample space, S={1,2,3,4,5,6}     |S|=6
Some events:
The number is odd = Eodd={1,3,5}     |Eodd|=3     P(Eodd)=|Eodd| / |S| = 3/6 = .5
Eeven={2,4,6}     Its probability is .5
E<3={1,2}     P(this event)=2/6=.333
E≥3={3,4,5,6} = complement of E<3     Probability=4/6=.66666 = 1-P(complement)

E7, rolling a 7={} the empty set. Probability is 0, impossible.
E123456, rolling a 1,2,3,4,5,or6={1,2,3,4,5,6}. Probability is 1, certain.

Probability experiment: roll two dice

Sample space S={
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
|S| = 36
Some events:
Sum of dice is 2={(1,1)}     P(this event)= 1/|S| = 1/36 = .02777
Sum of dice is 10={(4,6),(5,5),(6,4)}     Probability = ?
What is the probability of each of these events: sum is 2,3,4,5,6,7,8,9,10,11,12 ?
What is the probability of the event "sum is less than 5": ?

Probability experiment: flip three coins (or flip one coin three times).

Sample space: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}     |S|=8
Some events:
0 tails= {HHH}     Probability = 1/8=.125
1 tail= {HHT, HTH, THH}     Probability = 3/8=.375
2 tails= {HTT, THT, TTH}     Probability = 1/8=.375
3 tails= {TTT}     Probability = 1/8=.125
E≥1H At least one head: {HHH, HHT, HTH, HTT, THH, THT, TTH}     Probability = 7/8=.875 =1-P(~E≥1H) = 1-P(0 heads)
E≥2H = {HHH, HHT, HTH, THH} = 0 or 1 tails
First is a head and third is a head= {HHH, HTH}
First is a head or third is a head= {HHH, HTH, HHT, HTT, TTH, THH}
First is a head xor third is a head= {HHT, HTT, TTH, THH}
The coins are all the same = {HHH,TTT}

Probability experiment: flip four coins (or flip one coin four times).
Sample space: ?
Some events:
Probabilities of 0, 1, 2, 3, 4 tails: ?