You are throwing darts at a dart board. You have a 1/6 chance of striking the bull's-eye each time you throw. If you throw 3 times, what is the probability that you will strike the bull's-eye all 3 times?
1/216
To find the probability of striking the bull's-eye all three times, we'll multiply the individual probabilities of hitting the bull's-eye with each throw.
Given that you have a 1/6 chance of striking the bull's-eye each time, the probability can be calculated as follows:
P(Striking bull's-eye on first throw) = 1/6
P(Striking bull's-eye on second throw) = 1/6
P(Striking bull's-eye on third throw) = 1/6
The probability of striking the bull's-eye all three times can be calculated by multiplying these probabilities together:
P(Striking bull's-eye all three times) = P(Striking bull's-eye on first throw) * P(Striking bull's-eye on second throw) * P(Striking bull's-eye on third throw)
= (1/6) * (1/6) * (1/6)
= 1/216
Therefore, the probability of striking the bull's-eye all three times is 1/216.
To calculate the probability of striking the bull's-eye all 3 times, we need to multiply the probabilities of each individual dart hitting the bull's-eye.
Given that the probability of hitting the bull's-eye on each throw is 1/6, the probability of not hitting the bull's-eye (missing) on each throw would be 1 - 1/6 = 5/6.
Since each dart throw is independent of the others, we can multiply these probabilities together to find the joint probability:
P(all 3 hit) = P(hit on first throw) * P(hit on second throw) * P(hit on third throw)
= (1/6) * (1/6) * (1/6)
Calculating the equation, we have:
P(all 3 hit) = 1/216
So, the probability of striking the bull's-eye all 3 times is 1/216.