Exercise · ZW-ADDITION-RULE-009 · ★★★ Advanced
If \(P(A)=0.7\) and \(P(B)=0.6\), what is the smallest possible value of \(P(A\cap B)\)?
Choose one option.
Show answer
- C. \(0.3\)
Explanation
Since \(P(A\cup B)\le 1\), \(P(A\cap B)=1.3-P(A\cup B)\ge 0.3\). Zero is impossible here.
Review the concept: Addition rule
The addition rule gives the probability \(P\) that at least one of two events \(A\) and \(B\) occurs: add their probabilities and subtract that of their intersection.
\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]
More practice problems: addition rule
- ZW-ADDITION-RULE-001 If P(A)=0.5, P(B)=0.3 and P(A∩ B)=0.1, what is P(A∪ B)?
- ZW-ADDITION-RULE-002 A fair die is rolled. What is the probability of an even number or a multiple of 3?
- ZW-ADDITION-RULE-003 One card is drawn from a 52-card deck. What is the probability that it is a heart or a king?
- ZW-ADDITION-RULE-004 Events A and B are mutually exclusive, with P(A)=0.2 and P(B)=0.35. What is P(A∪ B)?
- ZW-ADDITION-RULE-005 If P(A)=0.5, P(B)=0.6 and P(A∪ B)=0.8, what is P(A∩ B)?
- ZW-ADDITION-RULE-006 Why is P(A∩ B) subtracted in the addition rule?
- ZW-ADDITION-RULE-007 In a group, 60% study English, 40% French and 25% both. What proportion study neither?
- ZW-ADDITION-RULE-008 Two fair dice are rolled. What is the probability that the sum is 7 or at least one die shows 6?