### Probability Question on Rolling a Number Cube**Question:**When rolling a fair, six-sided number cube, what is the probability of rolling an even number or a number less than 3?**Answer Choices:**- a) \(\frac{5}{6}\)- b) \(\frac{1}{2}\)- c) \(\frac{1}{3}\)- d) \(\frac{2}{3}\)**Solution Explanation:**To solve this probability question, consider the numbers on a six-sided number cube, which are {1, 2, 3, 4, 5, 6}.1. **Even Numbers:** The even numbers on a dice are 2, 4, and 6, so there are 3 even numbers.2. **Numbers Less Than 3:** The numbers on the dice that are less than 3 are 1 and 2, so there are 2 numbers less than 3.However, there's an overlap in these two sets (number 2), and it shouldn't be counted twice.3. **Total Outcomes:** - Even numbers: 2, 4, 6 (3 outcomes) - Less than 3: 1, 2 (2 outcomes) - Overlap: 2 (1 outcome)The probability can be calculated using the formula for the union of two sets:\[ P(A \cup B) = P(A) + P(B) - P(A \cap B)\]Where:- \(P(A)\) is the probability of selecting an even number = \(\frac{3}{6} = \frac{1}{2}\)- \(P(B)\) is the probability of selecting a number less than 3 = \(\frac{2}{6} = \frac{1}{3}\)- \(P(A \cap B)\) is the probability of selecting a number that is both even and less than 3 = \(\frac{1}{6}\)So, the probability is:\[ P(A \cup B) = \frac{1}{2} + \frac{1}{3} - \frac{1}{6}\]Finding a common denominator (6), we get:\[ P(A \cup B) = \frac{3}{6} + \frac{2}{6} - \frac{1}{6

Name: ### Probability Question on Rolling a Number Cube**Question:**When ro
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: ### Probability Question on Rolling a Number Cube**Question:**When rolling a fair, six-sided number cube, what is the probability of rolling an even number or a number less than 3?**Answer Choices:**- a) \(\frac{5}{6}\)- b) \(\frac{1}{2}\)- c) \(\fr