An unprepared student makes random guesses for the ten true or false questions on a quiz.find the probablity that there is at least one correct answer.
prob that he will get all of the wrong
= (1/2)^10 = 1/1024
so prob that he will get at least one correct
= 1 - 1/1024 = 1023/1024
Forever
To find the probability that there is at least one correct answer in the ten true or false questions, we need to calculate the probability of the complement event, which is the event of getting zero correct answers.
Since each question has two possible answers (true or false), the probability of guessing the correct answer for a single question is 1/2 or 0.5. Similarly, the probability of guessing incorrectly for a single question is also 1/2 or 0.5.
Now, let's calculate the probability of getting zero correct answers in the ten questions:
P(0 correct answers) = (0.5)^10
This is because, for each question, the probability of guessing incorrectly is 1/2 or 0.5, so we multiply this probability by itself for ten questions in a row. This gives us (0.5)^10.
To find the probability of getting at least one correct answer, we calculate the complement event:
P(at least one correct answer) = 1 - P(0 correct answers)
P(at least one correct answer) = 1 - (0.5)^10
Now, let's calculate the result:
P(at least one correct answer) = 1 - (0.5)^10
P(at least one correct answer) ≈ 1 - 0.0009765625
P(at least one correct answer) ≈ 0.9990234375
So, the probability that the unprepared student gets at least one correct answer is approximately 0.999 or about 99.9%.