a multiple-choice test consists of five questions, each with a-e answers.\nif you guess the answer to each…

Explanation:

Step1: Define binomial parameters

Number of trials $n=5$, probability of success $p=\frac{1}{5}=0.2$, probability of failure $q=1-p=0.8$. We calculate $P(X\geq3)=P(X=3)+P(X=4)+P(X=5)$ using the binomial formula $P(X=k)=\binom{n}{k}p^kq^{n-k}$.

Step2: Calculate P(X=3)

$$\binom{5}{3}(0.2)^3(0.8)^2 = 10\times0.008\times0.64 = 0.0512$$

Step3: Calculate P(X=4)

$$\binom{5}{4}(0.2)^4(0.8)^1 = 5\times0.0016\times0.8 = 0.0064$$

Step4: Calculate P(X=5)

$$\binom{5}{5}(0.2)^5(0.8)^0 = 1\times0.00032\times1 = 0.00032$$

Step5: Sum the probabilities

$$0.0512 + 0.0064 + 0.00032 = 0.05792$$ Convert to percentage: $0.05792\times100%\approx5.8%$, closest to 5.7%.

Answer:

b. 5.7%