Independent Events Math Example 3

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

Example 3

medium
A coin is flipped and a die is rolled. Find P(heads AND rolling a 6).

Solution

  1. 1
    Identify the events: Event A = heads on coin flip, Event B = rolling a 6 on a die.
  2. 2
    These events are independent because the coin outcome does not affect the die outcome. So P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times P(B).
  3. 3
    Calculate: P(heads)=12P(\text{heads}) = \frac{1}{2}, P(6)=16P(6) = \frac{1}{6}. Therefore P(heads AND 6)=12×16=112P(\text{heads AND 6}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}.

Answer

P(heads AND 6)=112≈0.0833P(\text{heads AND 6}) = \frac{1}{12} \approx 0.0833
When two events are independent, the probability of both occurring equals the product of their individual probabilities. The coin and die are physically separate experiments, so the outcome of one cannot influence the other — a textbook case of independence.

About Independent Events

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

Learn more about Independent Events →

More Independent Events Examples

Example 1 easy

A fair coin is flipped and a fair die is rolled. Find [formula].

Example 2 medium

For two events [formula] and [formula], [formula] and [formula]. If [formula] and [formula] are inde

Example 4 easy

A student randomly guesses on two multiple-choice questions, each with 4 options. Find the probabili

Example 5 hard

Events [formula] and [formula] satisfy [formula], [formula], and [formula]. Are [formula] and [formu

← All Independent Events Examples Independent Events Concept