Find the indicated probability.
An archer is able to hit the bull's-eye 53% of the time. If the archer shoots 10 arrows, what is the probability they get exactly 4 bull's-eyes? Assume each shot is independent of the others.
(1 point)
Responses
0.179
0.179
0.0789
0.0789
0.821
0.821
0.0905
0.0905
The probability of hitting the bull's-eye is 53% or 0.53. To find the probability of getting exactly 4 bull's-eyes out of 10 shots, we use the binomial probability formula.
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes
n is the number of trials (in this case, the number of shots)
k is the number of successes (in this case, 4 bull's-eyes)
p is the probability of success (in this case, 0.53)
Using this formula, we plug in the values:
P(X = 4) = C(10, 4) * (0.53)^4 * (1-0.53)^(10-4)
Calculating this gives us:
P(X = 4) = 210 * 0.53^4 * 0.47^6
P(X = 4) ≈ 0.179
So, the probability they get exactly 4 bull's-eyes out of 10 shots is approximately 0.179.