Independent Events Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

A fair coin is flipped and a fair die is rolled. Find

P(\text{Heads and a 4})

1
Identify the two events: $A = \text{Heads}$ , $B = \text{rolling a 4}$
2
Check independence: the coin flip does not affect the die roll, so $A$ and $B$ are independent
3
Find individual probabilities: $P(A) = \frac{1}{2}$ , $P(B) = \frac{1}{6}$
4
Apply multiplication rule: $P(A \cap B) = P(A) \cdot P(B) = \frac{1}{2} \cdot \frac{1}{6} = \frac{1}{12}$

Answer

P(\text{Heads and a 4}) = \frac{1}{12}

Two events are independent if the occurrence of one does not change the probability of the other. For independent events,

P(A \cap B) = P(A) \cdot P(B)

. Physical separation of experiments is the clearest indicator of independence.

About Independent Events

Two events are independent if the occurrence of one does not change the probability of the other: $P(A \cap B) = P(A) \cdot P(B)$ .

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