Let’s break down the process step-by-step to find out the probability of correctly guessing all five answers on a multiple-choice quiz, where each question has five possible choices.
### Step 1: Understand the Probability of a Single Correct Answer
For each question, there are 5 choices, with only one of them being correct. Therefore, the probability of guessing a single question correctly is given by:
[tex]\[
P(\text{correct answer}) = \frac{1}{5}
\][/tex]
### Step 2: Calculate the Probability of Getting All Five Questions Correct
Since each question is independent of the others, the probability of getting all five questions correct is the product of the probabilities of guessing each question correctly. This is calculated as follows:
[tex]\[
P(\text{correct all 5 answers}) = \left(\frac{1}{5}\right)^5
\][/tex]
### Step 3: Compute the Exact Probability
Let’s calculate:
[tex]\[
\left(\frac{1}{5}\right)^5 = \frac{1}{5 \times 5 \times 5 \times 5 \times 5} = \frac{1}{3125} = 0.00032
\][/tex]
So, the probability of guessing all five answers correctly is 0.00032.
### Step 4: Convert the Probability to a Percentage
To express this probability as a percentage, we multiply by 100:
[tex]\[
0.00032 \times 100 = 0.032\%
\][/tex]
### Step 5: Round to the Nearest Whole Number
When rounding 0.032% to the nearest whole number, we get:
[tex]\[
0\%
\][/tex]
### Conclusion
After following all the steps, we conclude that the probability of correctly guessing all five answers in a multiple-choice quiz with five questions, each having five choices, and rounding to the nearest whole number is:
[tex]\[
0\%
\][/tex]
