Math Problem Statement

A fair six-sided number cube (die) is rolled. Find the probability of getting less than a 6.

Solution

A fair six-sided die has numbers 1, 2, 3, 4, 5, and 6 on it. The probability of an event is calculated as:

Probability=Number of favorable outcomesTotal number of possible outcomes\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

In this case, you want to find the probability of rolling a number less than 6. The favorable outcomes are 1, 2, 3, 4, and 5, which are 5 possible outcomes.

The total number of possible outcomes is 6 (since the die has 6 faces).

Thus, the probability of getting a number less than 6 is:

P(less than 6)=56P(\text{less than 6}) = \frac{5}{6}

This simplifies to approximately:

P(less than 6)=0.8333P(\text{less than 6}) = 0.8333

So, the probability is 56\frac{5}{6} or approximately 83.33%.

Would you like further details or have any questions?

Here are 5 related questions:

  1. What is the probability of rolling a number greater than 4 on a six-sided die?
  2. If you roll two six-sided dice, what is the probability of both showing a number less than 6?
  3. How does the probability change if we roll an eight-sided die instead?
  4. What is the probability of rolling an even number on a six-sided die?
  5. What is the probability of rolling a number less than or equal to 3 on a six-sided die?

Tip: When solving probability problems, always check how many outcomes meet the condition you’re interested in and compare that to the total number of possible outcomes.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Basic Counting Principle

Formulas

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 5-7