A test has four questions: The first question is a true/false question, and it is followed by three multiple choice questions (answers a, b, c, d).
b. If a person guesses an answer for each question, what is the probability that he answers each question correctly?
For the true/false question, there is a 50% chance of guessing correctly.
For each of the multiple choice questions, there is a 25% chance of guessing correctly.
Therefore, the probability of guessing all four questions correctly is 0.5 x 0.25 x 0.25 x 0.25 = 0.0078125, or approximately 0.78%.
To calculate the probability that a person answers each question correctly, we need to know the probability of getting each question correct.
1. True/False Question: Since it has two possible answers (True or False) and the person is guessing, the probability of answering correctly is 1/2 or 0.5.
2. Multiple Choice Questions: Each multiple-choice question has four possible answers (a, b, c, d). Since the person is guessing, the probability of answering each question correctly is 1/4 or 0.25.
To find the probability of answering all four questions correctly, we multiply the probabilities of answering each individual question correctly.
Probability of answering all four questions correctly = (1/2) * (1/4) * (1/4) * (1/4)
= 1/128
Therefore, the probability that the person answers each question correctly when guessing is 1/128 or approximately 0.0078.