Question

ethan rolls a 6-sided number cube. what is the probability that he gets a number less than 3?

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

b. \\(\frac{5}{8}\\)

c. \\(\frac{2}{3}\\)

d. \\(\frac{1}{8}\\)

Explanation:

Step1: Determine total outcomes

A 6 - sided cube has numbers 1 - 6, so total outcomes \( n(S)=6 \).

Step2: Find favorable outcomes

Numbers less than 3 are 1, 2. So favorable outcomes \( n(A) = 2 \).

Step3: Calculate probability

Probability \( P(A)=\frac{n(A)}{n(S)}=\frac{2}{6}=\frac{1}{3} \). Wait, no, wait: Wait, numbers less than 3? Wait, 1 and 2 are less than 3, so 2 outcomes. Wait, but wait, the options: Wait, maybe a typo? Wait, the question says "less than 3"? Wait, 6 - sided cube, numbers 1,2,3,4,5,6. Numbers less than 3: 1,2. So probability is \( \frac{2}{6}=\frac{1}{3} \), which is option A? Wait, no, wait, maybe the question is "less than 3" or "less than 4"? Wait, no, the original question: "number less than 3"? Wait, 1 and 2 are less than 3, so 2 out of 6, which is \( \frac{1}{3} \), so option A.

Wait, let's re - check:
Total possible outcomes when rolling a 6 - sided cube: 6 (numbers 1, 2, 3, 4, 5, 6).
Favorable outcomes (numbers less than 3): 1, 2. So there are 2 favorable outcomes.
Probability \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{2}{6}=\frac{1}{3} \). So the correct option is A.

Answer:

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