Question

acob’s friend Adam did not study for a test and guesses on the last seven questions on a test. Each question is multiple choice and has 4 choices with exactly one correct answer per question. What is the probability that Adam will get 2 or fewer questions correctly? Round to the nearest hundredth at the very end and leave the final estimate as a decimal. 2

Answer 1

The probability that Adam will get 2 or fewer questions correctly is 0.4713.

Step-by-step explanation:

To find the probability that Adam will get 2 or fewer questions correctly, we need to consider the number of ways he can get 0, 1, or 2 questions correct out of the last 7 questions. Since there are 4 possible answers for each question and only 1 is correct, the probability of guessing a question correctly is 1/4. The probability of guessing a question incorrectly is 3/4.

To find the probability of getting 0 questions correct, we multiply the probability of guessing incorrectly for all 7 questions: (3/4)^7 = 0.1335 (rounded to four decimal places).

To find the probability of getting 1 question correct, we multiply the probability of guessing correctly once and incorrectly for the remaining 6 questions: (1/4) * (3/4)^6 = 0.2502 (rounded to four decimal places).

To find the probability of getting 2 questions correct, we multiply the probability of guessing correctly twice and incorrectly for the remaining 5 questions: (1/4)^2 * (3/4)^5 = 0.0876 (rounded to four decimal places).

Finally, we add the probabilities of getting 0, 1, or 2 questions correct: 0.1335 + 0.2502 + 0.0876 = 0.4713 (rounded to four decimal places).