Two events are independent when the result of one event does not affect the result of the other event.
An event becomes dependent when the result of a an earlier events affects the result of the subsequent event.
Typically, events become dependent when the total number of possibilities change between events.
A bag contains 5 red balls and 3 green balls. A red ball is drawn and replaced. What is the probability of selecting a red ball on a second draw?
The events are independent. The probability of selecting a red ball on the second draw is 5 out of 8, or `frac(5)(8)`
Answer: `frac(5)(8)`
A bag contains 5 red balls and 3 green balls. A red ball is drawn and is not replaced. What is the probability of selecting a red ball on a second draw?
The events are dependent, as there are now only 4 red balls in the bag, and a total of 7 balls altogether. The probability of drawing a second red ball is now 4 out of 7, or `frac(4)(7)`.
If a green ball had been drawn first, then the probability of drawing a red ball as the second ball would be different.
Answer: `frac(4)(7)`