Question

test 2
score: 6/10 answered: 6/10
question 7
a quick quiz consists of a multiple - choice question with 6 possible answers followed by a multiple - choice question with 4 possible answers. if both questions are answered with random guesses, find the probability that both responses are correct.
report the answer as a percent rounded to one decimal place accuracy. you need not enter the \%\ symbol.
prob = %
question help: video

Explanation:

Step1: Calculate the probability of getting the first question right

The probability of getting a multiple - choice question with 6 possible answers right is \(p_1=\frac{1}{6}\).

Step2: Calculate the probability of getting the second question right

The probability of getting a multiple - choice question with 4 possible answers right is \(p_2 = \frac{1}{4}\).

Step3: Use the multiplication rule for independent events

Since the two questions are independent events, the probability that both are correct is \(p=p_1\times p_2\).
Substitute \(p_1=\frac{1}{6}\) and \(p_2=\frac{1}{4}\) into the formula: \(p=\frac{1}{6}\times\frac{1}{4}=\frac{1}{24}\).

Step4: Convert the fraction to a percentage

To convert \(\frac{1}{24}\) to a percentage, use the formula \(percentage=\frac{1}{24}\times100\%\).
\(\frac{1}{24}\times100\%=\frac{100}{24}\% \approx 4.2\%\)

Answer:

4.2