To solve the problem of finding the probability of striking the bull's-eye all 3 times when the probability of hitting the bull's-eye in a single throw is [tex]\(\frac{1}{6}\)[/tex], we need to calculate the combined probability for these independent events.
The probability of hitting the bull's-eye in a single throw is:
[tex]\[ \frac{1}{6} \][/tex]
Since the events are independent, the probability of all three strikes hitting the bull's-eye (i.e., hitting the bull's-eye every time in 3 throws) is the product of the individual probabilities:
[tex]\[ \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right) \][/tex]
Performing the multiplication of these fractions:
[tex]\[ \left( \frac{1}{6} \right)^3 = \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} = \frac{1}{216} \][/tex]
Thus, the probability that you will strike the bull's-eye all 3 times is:
[tex]\[ \frac{1}{216} \][/tex]
Therefore, the correct answer is:
B. [tex]\(\frac{1}{216}\)[/tex]
