Math Problem Statement

Find the probability of rolling a 4 the first time and a 1 the second time when a single die is rolled twice.

Solution

The problem asks for the probability of rolling a 4 on the first roll and a 1 on the second roll with a single die rolled twice.


Solution:

  1. Probability of rolling a 4 on the first roll:
    A standard die has 6 faces (1 through 6), so the probability of rolling a 4 is:
    P(4)=16P(\text{4}) = \frac{1}{6}

  2. Probability of rolling a 1 on the second roll:
    Similarly, the probability of rolling a 1 is:
    P(1)=16P(\text{1}) = \frac{1}{6}

  3. Combined probability:
    Since the rolls are independent, we multiply the probabilities:
    P(4 on 1st roll and 1 on 2nd roll)=P(4)×P(1)=16×16=136.P(\text{4 on 1st roll and 1 on 2nd roll}) = P(\text{4}) \times P(\text{1}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}.


Final Answer:

136\frac{1}{36}

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Related Questions:

  1. What is the probability of rolling a 6 on both rolls?
  2. What is the probability of not rolling a 4 on the first roll?
  3. What is the probability of rolling two different numbers?
  4. What is the probability of rolling at least one 1 in two rolls?
  5. What is the probability of rolling a total sum of 5 in two rolls?

Tip: When dealing with independent events, always multiply their individual probabilities to find the combined probability.

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Events

Formulas

P(A and B) = P(A) × P(B)
Probability of rolling a specific outcome on a die = 1/6

Theorems

Law of Independent Events

Suitable Grade Level

Grades 6-8