Math Problem Statement

For the experiment of rolling a single fair die, find the probability of obtaining not less than 5.

Solution

The problem asks for the probability of obtaining a value "not less than 5" when rolling a single fair die.

A standard die has six faces, numbered 1 through 6. The numbers that are not less than 5 are 5 and 6.

Step-by-step solution:

  1. Favorable outcomes: The possible outcomes where the roll is 5 or greater are {5, 6}.

    • So, there are 2 favorable outcomes.
  2. Total possible outcomes: When rolling a die, there are 6 equally likely outcomes in total (1 through 6).

  3. Probability formula: The probability PP of an event is given by: P(event)=Number of favorable outcomesTotal number of possible outcomesP(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

  4. Apply the values: P(not less than 5)=26=13P(\text{not less than 5}) = \frac{2}{6} = \frac{1}{3}

So, the probability of obtaining a number not less than 5 is 1/3.

Would you like more details, or do you have any questions?

Here are five related questions to think about:

  1. What is the probability of rolling an even number on a fair die?
  2. What is the probability of rolling a number less than 4?
  3. If you roll two dice, what is the probability that the sum is 7?
  4. How would the probability change if the die was not fair?
  5. What is the probability of rolling a 5 twice in a row?

Tip: Simplify probabilities as much as possible to their lowest terms for clarity and correctness!

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

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

Theorems

Basic Probability Theory

Suitable Grade Level

Grades 5-7