Exercise · ZW-PROBABILITY-MEASURE-003 · ★☆☆ Basic
Let \(\Omega=\{a,b,c\}\). Which assignment for \((P(a),P(b),P(c))\) defines a probability measure?
Choose one option.
Show answer
- C. \((0.5,\,0.3,\,0.2)\)
Explanation
Values must be nonnegative and add up to 1. Only \(0.5+0.3+0.2=1\) works; the others add up to \(1.2\), to \(1\) with a negative value, or to \(0.9\).
Review the concept: Probability measure
A probability measure \(P\) is a function that assigns to each event \(A\) a number between 0 and 1, equals 1 on the sample space \(\Omega\) and adds over mutually exclusive events.
\[P(\Omega)=1,\qquad P\Big(\bigcup_i A_i\Big)=\sum_i P(A_i)\]
More practice problems: probability measure
- ZW-PROBABILITY-MEASURE-001 A fair die has P(\k\)=16 for each face. What is P(\2,4,6\)?
- ZW-PROBABILITY-MEASURE-002 If A and B are mutually exclusive with P(A)=0.3 and P(B)=0.5, what is P(A∪ B)?
- ZW-PROBABILITY-MEASURE-004 If P(A)=0.35, what is P(A^c)?
- ZW-PROBABILITY-MEASURE-005 Which of these values cannot be the probability of any event?
- ZW-PROBABILITY-MEASURE-006 If P(A)=0.4, P(B)=0.5 and P(A∩ B)=0.2, what is P(A∪ B)?
- ZW-PROBABILITY-MEASURE-007 If A⊆ B, P(A)=0.3 and P(B)=0.5, what is P(Bsetminus A)?
- ZW-PROBABILITY-MEASURE-008 It is known that P(A)=0.5, P(B)=0.6 and P(A∪ B)=0.9. What is P(A∩ B)?
- ZW-PROBABILITY-MEASURE-009 If P(A)=0.6 and P(B)=0.7, what is the smallest possible value of P(A∩ B)?