Question

a quick quiz consists of a multiple - choice question with 5 possible answers followed by a multiple - choice question with 6 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 two decimal place accuracy. you need not enter the “%” symbol. probability =

Explanation:

Step1: Calculate probability of first - question correct

The probability of getting the first multiple - choice question (with 5 possible answers) correct by random guess is $\frac{1}{5}=0.2$.

Step2: Calculate probability of second - question correct

The probability of getting the second multiple - choice question (with 6 possible answers) correct by random guess is $\frac{1}{6}\approx0.1667$.

Step3: Calculate probability of both correct

Since the two events are independent, the probability that both responses are correct is the product of their individual probabilities. So $P = \frac{1}{5}\times\frac{1}{6}=\frac{1}{30}\approx0.0333$.

Step4: Convert to percentage

To convert the probability to a percentage, multiply by 100. So $0.0333\times100 = 3.33\%$.

Answer:

3.33