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Probability Basics
Probability Basics
Probability measures how likely an event is, with values between $0$ and $1$.
Core Rules
$$P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}}$$
$$P(A^c)=1-P(A)$$
$$P(A \cup B)=P(A)+P(B)-P(A \cap B)$$
Example 1
What is the probability of rolling a 4 on a fair die?
$\frac{1}{6}$.
Example 2
What is the probability of drawing a heart from a standard deck?
$\frac{13}{52}=\frac{1}{4}$.
Independence
If $A$ and $B$ are independent, then $$P(A \cap B)=P(A)P(B).$$
Practice Problems
1. Probability of flipping heads.
2. Probability of not rolling a 6.
3. If $P(A)=0.3$, find $P(A^c)$.
4. State the multiplication rule for independent events.
5. Probability of drawing a king from a deck.
Show Answer Key
1. $\frac{1}{2}$
2. $\frac{5}{6}$
3. $0.7$
4. $P(A \cap B)=P(A)P(B)$
5. $\frac{4}{52}=\frac{1}{13}$