SOLUTION: Probability questions have always given me trouble. Help with this problem would be greatly appreciated! A test has 15 multiple choice questions, each question having 4 possible

Question 1131017: Probability questions have always given me trouble. Help with this problem would be greatly appreciated!
A test has 15 multiple choice questions, each question having 4 possible answers and only one of which is correct out of the 4 options. What is the probability that the test taker randomly guesses the right answer on one of the questions and gets the question correct? What is the probability that the test taker randomly guesses the right answer on one of the questions and gets the question wrong? What is the probability that the test taker guesses at all 15 questions and gets at least one of them right?
Thank you!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
This problem requires the use of the Binomial Probability formula
:
Probability (P) (k successes out of n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n!/(k! * (n-k)!), p is the probability of a success
:
P for guessing an answer correctly is 1/4
:
P for guessing an answer incorrectly is 1 - 1/4 = 3/4
:
P ( at least 1 success in 15 trials) = 1 - P(0 successes in 15 trials) = 1 - 15C0 * (1/4)^0 * (3/4)^(15-0) = 1 - 0.01 = 0.99
:
Note "at least one of them right" means 1 or 2 or 3 or 4 ...... or 15
:

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