Exercise · ZW-CONDITIONAL-PROBABILITY-004 · ★☆☆ Basic
If \(P(A)=0.6\), \(P(B)=0.4\) and \(P(A\cup B)=0.7\), what is \(P(A\mid B)\)?
Choose one option.
Show answer
- A. 0.75
Explanation
By the addition rule, \(P(A\cap B)=0.6+0.4-0.7=0.3\). Then \(P(A\mid B)=0.3/0.4=0.75\). Dividing by \(P(A\cup B)\) would give 0.43, which is something else.
Review the concept: Conditional probability
The conditional probability of \(A\) given \(B\), \(P(A\mid B)\), is the probability that \(A\) occurs when \(B\) is already known to have occurred; it is computed within the space reduced to \(B\).
\[P(A\mid B)=\frac{P(A\cap B)}{P(B)},\qquad P(B)>0\]
More practice problems: conditional probability
- ZW-CONDITIONAL-PROBABILITY-001 If P(A∩ B)=0.2 and P(B)=0.5, what is P(A| B)?
- ZW-CONDITIONAL-PROBABILITY-002 A fair die is rolled and it is known the result is even. What is the probability that it is 6?
- ZW-CONDITIONAL-PROBABILITY-003 Two fair dice are rolled and the first shows 3. What is the probability that the sum is 8?
- ZW-CONDITIONAL-PROBABILITY-005 An urn has 5 red and 3 blue balls. Two are drawn without replacement. Given that the first was red,…
- ZW-CONDITIONAL-PROBABILITY-006 Two cards are drawn from a 52-card deck without replacement. What is the probability that both are…
- ZW-CONDITIONAL-PROBABILITY-007 A family has two children and at least one is a girl. Assuming each child is equally likely to be a…
- ZW-CONDITIONAL-PROBABILITY-008 If P(A)=0.4 and P(B| A)=0.5, what is P(A∩ B)?
- ZW-CONDITIONAL-PROBABILITY-009 With P(B)>0, which statement is true?
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