Question

1. which of the following values represent impossible events?

a. 0
b. 1
c. \\( \frac { 1 } { 4 } \\)
d. \\( \frac { 1 } { 2 } \\)

Explanation:

Step1: Recall probability range

The probability \(P(E)\) of an event \(E\) satisfies \(0\leq P(E)\leq1\). An impossible event has probability \(P(E) = 0\), a certain event has \(P(E)=1\), and \(0 < P(E)<1\) for possible non - certain events.

Step2: Analyze each option

• Option a: \(P = 0\) represents an impossible event.
• Option b: \(P = 1\) represents a certain event.
• Option c: \(P=\frac{1}{4}=0.25\) is a possible event (\(0 < 0.25<1\)).
• Option d: \(P=\frac{1}{2}=0.5\) is a possible event (\(0 < 0.5<1\)).

Answer:

A. 0