independent

Multiplication principle
If there are p experiments and the first has n_1 equally likely outcomes, the second has n_2 equally likely outcomes, and so on until the pth experiment has n_p equally likely outcomes, then there are
n_1×n_2×....×n_p =?_(i=1)^p?n_i
equally likely possible outcomes for the p experiments.

Example
A class of school children consists of 14 boys and 17 girls. The teacher wishes to pick one boy and one girl to star in the school play.
By the multiplication principle, she can do this in 14×17 = 238 different ways.

The multiplication rule
The formula for conditional probability is useful when we want to calculate P (A|B) from P (A?B) and P (B). However, more commonly we want to know P (A?B) and we know P (A|B) and P (B).
A simple rearrangement gives us the multiplication rule.
P (A?B) = P (B) × P (A|B)
The multiplication rule generalizes to more than two events.
For example, for three events we have,
P (A_1 ?A_2 ?A_3) =P (A_1) P (A_2 |A_1) P (A_3|A_1 ?A_2)

Examples
What is the probability of getting an odd number when throwing dice
P (1 or 3 or 5) =p (1) +p (3) +p (5)
= 1/6+1/6+1/6=1/2 (these are mutually exclusive)
What is the probability of getting two faces are similar when rolling the dice twice
P[(1,1) or (2,2)or (3,3) ….or(6,6)]=[p(1,1)+p(2,2)+p(3,3)+…+p(6,6)]
=1/36+1/36+?..+1/36=6/36=1/6 (these are mutually exclusive)