Question

An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer.

Could some one please help me?
And explain to me how they got the answer?

and is there another way besides the tree method?

Answer 1

Take 10/2=5
possibility of 5 right or 5 wrong because there is only two possible outcomes
2/100 = .50 (True and False Outcomes)
There are a total of 10 questions
.50^10 questions = .0009765625 rounded = .0009777
use the complement formula 1-P=
1-.0009777 = .9990223 that there is at least once correct answer

Answer 2

All we have to exclude is the case when he guessed all of them wrong
that prob would be (1/2)^10 = 1/1024

so the prob of getting at least one correct is 1 - 1/1024 = 1023/1024