A single die is rolled 3 times. Find the probability of rolling one 1 times.
State answer as a decimal rounded to six decimal places.

Question

A single die is rolled 3 times. Find the probability of rolling one 1 times. State answer as a decimal rounded to six decimal places.

UpStudy AI · Accepted Answer

To find the probability of rolling exactly one **1** in three rolls of a single die, we can use the binomial probability formula:

$$
P(X = k) = \binom{n}{k} \left(\frac{1}{6}\right)^k \left(\frac{5}{6}\right)^{n-k}
$$

Where:
- $$ n = 3 $$ (number of trials)
- $$ k = 1 $$ (number of successful outcomes, i.e., rolling a **1**)
- $$ \frac{1}{6} $$ is the probability of rolling a **1** on a single die
- $$ \frac{5}{6} $$ is the probability of not rolling a **1**

Plugging in the values:

$$
P(X = 1) = \binom{3}{1} \left(\frac{1}{6}\right)^1 \left(\frac{5}{6}\right)^2 = 3 \times \frac{1}{6} \times \frac{25}{36} = \frac{75}{216} \approx 0.347222
$$

**Answer:**  
0.347222
The probability of rolling exactly one **1** in three dice rolls is approximately **0.347222**.

A single die is rolled 3 times. Find the probability of rolling one 1 times.
State answer as a decimal rounded to six decimal places.

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