Final answer:
The probability of three wrong guesses followed by a correct guess is calculated as (1-p)³ * p, and the probability of getting exactly one correct answer is 4 * (1-p)³ * p, both rounded to four decimal places.
Step-by-step explanation:
To calculate the probability that the first three guesses are wrong and the fourth is correct, denoted P(WWWC), we assume that each guess is independent of the others. If the probability of guessing correctly is 'p' and incorrectly is '1-p', then P(WWWC) = (1-p)³ * p. To determine the probability of getting exactly one correct answer out of four guesses, we notice that there are four possible sequences where we have one correct guess (CWWW, WCWW, WWCW, WWWC), each with the same probability of occurring. Thus, the probability is 4 * (1-p)³ * p.
Remember, you should round answers to relative frequency and probability problems to four decimal places. When using a calculator or software, you can input the probabilities to find exact values for P(WWWC) and the exact probability of getting one correct answer.
In terms of a multiple choice exam with three choices per question, if each choice is equally likely, 'p' would be 1/3 and '1-p' would be 2/3. Therefore, P(WWWC) = (2/3)^3 * (1/3), and the probability of getting exactly one correct answer is 4 * (2/3)^3 * (1/3).