Question

which of the following probabilities indicates a certain event?
a. 1
b. \frac{3}{4}
c. \frac{1}{2}
d. \frac{1}{3}

Explanation:

Step1: Recall probability range

Probability of an event \(P(E)\) satisfies \(0\leq P(E)\leq1\). A certain event has \(P(E) = 1\).

Step2: Check each option

• Option a: \(P = 1\), which is for a certain event.
• Option b: \(P=\frac{3}{4}<1\), not a certain event.
• Option c: \(P=\frac{1}{2}<1\), not a certain event.
• Option d: \(P=\frac{1}{3}<1\), not a certain event.

Answer:

A. 1