Question

Please answer all I will rate your solution

An archer is able to hit the bull's-eye 56% of the time. If she shoots 8 arrows, what is the probability that she gets at least 2 bull'seyes? Assume each shot is independent of the others. Exp

Answer 1

The probability of an archer getting at least 2 bull's-eyes out of 8 shots, with each shot having a success rate of 56%, can be calculated using the binomial probability formula.

Step-by-step explanation:

To solve for the probability that an archer gets at least 2 bull's-eyes when shooting 8 arrows with a success rate of 56%, we can use the binomial probability formula.

Calculation Steps

1. Identify the success probability (p) for one arrow, which is 0.56.
2. Calculate the probability of getting exactly 0 and exactly 1 bull's-eye, which we need to subtract from 1 to find at least 2 bull's-eyes.
3. Use the binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time.
4. Find P(X=0) and P(X=1).
5. Calculate 1 - (P(X=0) + P(X=1)) to get the probability of getting at least 2 bull's-eyes.

By completing the calculations:

• P(X=0) = C(8, 0) * (0.56)^0 * (0.44)^8
• P(X=1) = C(8, 1) * (0.56)^1 * (0.44)^7
• P(at least 2) = 1 - (P(X=0) + P(X=1))

After substitution and simplification, we will obtain the probability that the archer hits at least 2 bull's-eyes.