Determine the probability of getting a single question correct and incorrect.

Question

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To find the probability that Lorenzo will get at least one correct answer, we can use the complement rule. The probability of getting at least one correct answer is equal to 1 minus the probability of getting zero correct answers (i.e., all answers incorrect).

Determine the probability of getting a single question correct and incorrect.
There are four options for each question, and only one is correct.
The probability of getting a question correct is $P(\text{correct}) = \frac{1}{4} = 0.25$ .
The probability of getting a question incorrect is $P(\text{incorrect}) = 1 - P(\text{correct}) = 1 - \frac{1}{4} = \frac{3}{4} = 0.75$ .
Calculate the probability of getting all five questions incorrect.
Since there are five questions and each is independent, the probability of getting all five incorrect is:
$P(\text{all incorrect}) = (P(\text{incorrect}))^5$ $P(\text{all incorrect}) = \left(\frac{3}{4}\right)^5$ $P(\text{all incorrect}) = (0.75)^5$ $P(\text{all incorrect}) = 0.75 \times 0.75 \times 0.75 \times 0.75 \times 0.75$ $P(\text{all incorrect}) = 0.2373046875$
Calculate the probability of getting at least one correct answer.
Using the complement rule:
$P(\text{at least one correct}) = 1 - P(\text{all incorrect})$ $P(\text{at least one correct}) = 1 - 0.2373046875$ $P(\text{at least one correct}) = 0.7626953125$
Round the probability to three decimal places and select the corresponding option.
Rounding 0.7626953125 to three decimal places gives 0.763.
This matches option C.

The final answer is $\text{C. 0.763}$ .

Determine the probability of getting a single question correct and incorrect.

Answer

Step-by-step solution

Determine the probability of getting a single question correct and incorrect.

Calculate the probability of getting all five questions incorrect.

Calculate the probability of getting at least one correct answer.

Round the probability to three decimal places and select the corresponding option.

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