Question

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

Answer 1

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.