What is Probability?
Before we dive into dependent and independent events, let's make sure we're on the same page about probability itself.
A measure of how likely an event is to occur, expressed as a number between 0 and 1 (or as a percentage between 0% and 100%).
A probability of 0 means the event is impossible, while a probability of 1 means it is certain. Most events fall somewhere in between.
We calculate the probability of a single event using:
Think of probability like a weather forecast. When the meteorologist says there's a 70% chance of rain, they're saying that out of many similar days with the same conditions, about 70 out of 100 would produce rain.
In this subtopic, we'll explore what happens when we deal with two or more events happening together — and how the relationship between those events changes the way we calculate probability.
Independent Events
Two events are independent if the outcome of one event does not affect the outcome of the other event.
This is a crucial concept. When events are independent, knowing the result of the first event gives you zero information about what will happen in the second event.
Examples of independent events:
- Flipping a coin and then rolling a die — the coin result doesn't change what the die shows
- Drawing a card from a deck, replacing it, then drawing again
- The probability of it raining today and the probability of you scoring a goal in football practice
- Rolling a die twice — the first roll doesn't influence the second
A helpful test: ask yourself, "Does the first event change the conditions for the second event?" If the answer is no, the events are independent.
11 more sections in this topic
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