Exercise · ZW-INDEPENDENCE-OF-EVENTS-003 · ★☆☆ Basic
If \(P(A)=0.4\), \(P(B)=0.5\) and \(P(A\cap B)=0.2\), are they independent?
Choose one option.
Show answer
- A. Yes, because \(0.2=0.4\cdot0.5\)
Explanation
The definition requires \(P(A\cap B)=P(A)P(B)\), and here \(0.4\cdot0.5=0.2\). A positive intersection, or one smaller than \(P(B)\), decides nothing.
Review the concept: Independence of events
Two events \(A\) and \(B\) are independent when knowing that one occurred does not change the probability \(P\) of the other.
\[P(A\cap B)=P(A)\,P(B)\]
More practice problems: independence of events
- ZW-INDEPENDENCE-OF-EVENTS-001 If A and B are independent with P(A)=0.3 and P(B)=0.5, what is P(A∩ B)?
- ZW-INDEPENDENCE-OF-EVENTS-002 Two fair coins are tossed. What is the probability of getting two heads?
- ZW-INDEPENDENCE-OF-EVENTS-004 If P(A)=0.5, P(B)=0.4 and P(A∩ B)=0.3, which statement is correct?
- ZW-INDEPENDENCE-OF-EVENTS-005 If A and B are independent with P(A)=0.6 and P(B)=0.5, what is P(A| B)?
- ZW-INDEPENDENCE-OF-EVENTS-006 If A and B are independent with P(A)=0.3 and P(B)=0.2, what is P(A∪ B)?
- ZW-INDEPENDENCE-OF-EVENTS-007 A fair coin is tossed three times. What is the probability of at least one head?
- ZW-INDEPENDENCE-OF-EVENTS-008 A fair die is rolled. Let A: «even» and B: «1 or 2». Are they independent?
- ZW-INDEPENDENCE-OF-EVENTS-009 Let A and B be independent events with positive probabilities. Can they be mutually exclusive?
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