Probability — Addition Theorem & Conditional explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Probability helps us measure chance in a careful way.
After basic probability, students learn how to work with combined events and conditional events.
These ideas are used in cards, dice, surveys, games, risk, and decisioaking.
A sample space is the set of all possible outcomes. An event is a part of the sample space.
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The complement of an event means the event does not happen.
When two events are combined with "or", we must avoid doublounting outcomes that belong to both events.
Conditional probability means the chance of one event when another event is already known.
Two events are independent if knowing one event happened does not change the probability of the other event.
Meaning: A complementary event means not happening.
Definition: The complement of A is the event that A does not occur.
If A is getting a head, not A is getting a tail.
Meaning: The addition theorem finds the chance that A or B happens.
Definition: .
We subtract P(A and B) because it was counted twice.
Meaning: Mutually exclusive events cannot happen together.
Definition: A and B are mutually exclusive if .
On one die roll, getting 2 and getting 5 cannot happen together.
Meaning: Conditional probability uses extra information.
Definition: P(A given B) means probability of A when B has already happened.
If we know a card is red, the chance that it is a heart is found only from the red cards.
Easy
Question: If .7, find P(not A).
Medium
Question: If .4, .5, and .2, find P(A or B).
Exam-level
Question: If .18 and .6, find P(A given B).
Adding probabilities without subtracting overlap
Why it happens: The shared part is counted twice.
Correct approach: Use .
Using the original sample space for conditional probability
Why it happens: The condition is ignored.
Correct approach: Restrict the sample space to the given condition.
Assuming events are independent
Why it happens: Independence sounds natural but may not be true.
Correct approach: Check whether one event affects the other.
Getting a probability outside 0 to 1
Why it happens: Values are added, subtracted, or divided in the wrong order.
Correct approach: Probability must stay between 0 and 1.
What does A or B mean in probability?
It means A happens, B happens, or both happen.
Why do we subtract P(A and B)?
Because the overlap is counted once in P(A) and once again in P(B).
What does given mean?
It means we already know one event happened, so we use that smaller group.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.
Meaning: Independent events do not affect each other.
Definition: A and B are independent if x P(B).
Two tosses of a fair coin are independent because the first toss does not change the second toss.