To determine the probability of striking the bull's-eye 3 times in a row when you have a [tex]\(\frac{1}{6}\)[/tex] chance to hit it each time, follow these steps:
1. Identify the probability of hitting the bull's-eye in a single throw:
The probability of hitting the bull's-eye with one throw is:
[tex]\[
\text{Probability} (\text{Single Throw}) = \frac{1}{6}
\][/tex]
2. Calculate the probability of hitting the bull's-eye 3 times consecutively:
Since each throw is an independent event, the probability of hitting the bull's-eye 3 times in a row is the product of the probabilities of each individual throw.
[tex]\[
\text{Probability} (\text{3 Throws}) = \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right)
\][/tex]
Simplify this:
[tex]\[
\left( \frac{1}{6} \right)^3 = \frac{1}{216}
\][/tex]
3. Compare the calculated probability with the given choices:
The calculated probability of hitting the bull's-eye 3 times in a row is [tex]\(\frac{1}{216}\)[/tex]. Now, compare this with the answer choices provided:
- A. [tex]\(\frac{5}{136} \approx 0.0367647\)[/tex]
- B. [tex]\(\frac{1}{210} \approx 0.0047619\)[/tex]
- C. [tex]\(\frac{3}{233} \approx 0.0128756\)[/tex]
- D. [tex]\(\frac{1}{100} = 0.01\)[/tex]
4. Identify the correct choice:
The choice that matches [tex]\(\frac{1}{216}\)[/tex] most closely is:
[tex]\[
\text{Choice B:} \frac{1}{210} \approx 0.0047619
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{B. \frac{1}{210}}
\][/tex]
