Probability and Non-Probability Sampling
Two or more events are independent if the occurrence of one event has no influence on the occurrence of the other event(s). Let us put this in annotations:
$$ \text P( \text A | \text B) = \text P(\text A) $$
or
$$ \text P(\text B | \text A) = \text P(\text B) $$
If this condition is not satisfied, the events are said to be dependent.
Suppose you rolled a die and flipped a coin, the probability of getting any number face on the die would not influence the probability of getting a head or a tail on the coin. The two events are independent.
Suppose you have a bag containing 8 green balls and 5 blue balls. If you draw a blue ball without replacing it, the probability of drawing another blue ball in your second attempt is greatly changed because you drew a blue ball the first time. Such events are said to be dependent.
Question
Mike Jamerson tosses a coin twice. What is the probability of getting a head on the first toss and a head on the second toss?
A. 1/2
B. 1/4
C. 2/3
Solution
The correct answer is B.
The coin has no memory. Therefore, the first outcome has no influence on the second outcome. Thus:
$$ \begin{align*}
\text P(\text{head and head}) & = \text P(\text H) * \text P(\text H) \\
& =\cfrac {1}{2} * \cfrac {1}{2} \\
& = \cfrac {1}{4} \\
\end{align*} $$Note: If two events are independent:
$$ \text P(\text{AB}) =\text P( \text A) * \text P(\text B) $$
Reading 8 LOS 8g
Distinguish between dependent and independent events