What is the probability that all answers will be correct?

Question

IF a student takes a test consisting of 2o true false questions and randomly guesses at all of the answers, what is the probability that all the answers will be correct?

 

Answer 1

The rule to remember and apply in this type of problem is that when you have several independent events, the probability of all of them occurring is the product of the individual probabilities.  In this problem, the events are independent, since guessing the answer for one question does not impact the guess for the answer of another question.  Since there are only 2 possible choices for each question, the probability of guessing one answer correctly is 0.5, which you must elevate to the power equal to the number of questions being guessed.  Hence you get

 

P = (0.5)²⁰,

 

which is an extremely small number, since you are multiplying a long chain of numbers that are less than 1, making the product even smaller still with each multiplication.

Answer 2

P = (1/2) (1/2) (1/2) ....... 20 times =  (1/2)²⁰