Question

1. what is the probability of rolling either a 2 or a 5 on a six - sided die?

a. $\frac{1}{12}$
b. $\frac{1}{3}$
c. $\frac{1}{6}$
d. $\frac{1}{5}$

Explanation:

Step1: Determine total number of outcomes

A six - sided die has \(n(S)=6\) possible outcomes (\(1,2,3,4,5,6\)).

Step2: Determine number of favorable outcomes

The favorable outcomes (rolling a \(2\) or a \(5\)) are \(n(E) = 2\) (the outcomes \(2\) and \(5\)).

Step3: Use probability formula

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substitute \(n(E) = 2\) and \(n(S)=6\) into the formula: \(P(E)=\frac{2}{6}=\frac{1}{3}\).

Answer:

B. \(\frac{1}{3}\)