Math Problem Statement

Ralph rolls a single die two times in a row. What is the probability that he will roll a 'three' both times?

Solution

To solve this probability problem, we need to determine the likelihood that Ralph will roll a "three" on a die both times.

Each die roll is independent, and the probability of rolling a "three" on a single roll of a standard six-sided die is 16\frac{1}{6}.

Since the rolls are independent, we multiply the probabilities of each event happening:

Probability of rolling a three twice=16×16=136\text{Probability of rolling a three twice} = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}

Therefore, the correct answer is:

C: 136\frac{1}{36}

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

Here are some related questions:

  1. What is the probability of rolling the same number twice in a row with a die?
  2. How would the probability change if Ralph rolled the die three times and wanted all threes?
  3. What is the probability of rolling a number less than three on two consecutive rolls?
  4. How does the probability change if using a different-sided die, like an 8-sided die?
  5. What is the probability of rolling an even number twice in a row?

Tip: In probability, when dealing with independent events, always multiply the probabilities of each event occurring.

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Events

Formulas

Probability of two independent events: P(A and B) = P(A) * P(B)

Theorems

Law of Independent Probability

Suitable Grade Level

Grades 6-8