Independent Events Math Example 2

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Example 2

medium
For two events AA and BB, P(A)=0.4P(A) = 0.4 and P(B)=0.5P(B) = 0.5. If AA and BB are independent, find (a) P(A∩B)P(A \cap B) and (b) P(A∪B)P(A \cup B).

Solution

  1. 1
    (a) Use independence: P(A∩B)=P(A)⋅P(B)=0.4×0.5=0.20P(A \cap B) = P(A) \cdot P(B) = 0.4 \times 0.5 = 0.20
  2. 2
    (b) Apply the addition rule: P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)
  3. 3
    Substitute: P(A∪B)=0.4+0.5−0.20=0.70P(A \cup B) = 0.4 + 0.5 - 0.20 = 0.70
  4. 4
    Verify: P(A∪B)=0.70≤1P(A \cup B) = 0.70 \leq 1 ✓

Answer

P(A∩B)=0.20P(A \cap B) = 0.20; P(A∪B)=0.70P(A \cup B) = 0.70
Independence simplifies intersection calculations. The union formula P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B) prevents double-counting outcomes in both events. Always subtract the intersection.

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 3 medium

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

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

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