Question

A student is taking a​ multiple-choice exam in which each question has two choices. Assuming that she has no knowledge of the correct answers to any of the​ questions, she has decided on a strategy in which she will place two balls​ (marked Upper A and Upper B​) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are four ​multiple-choice questions on the exam. Complete parts​ (a) through​ (d) below. a. What is the probability that she will get four questions​ correct? nothing ​(Round to four decimal places as​ needed.)

Answer 1

Answer: Hi!

So if in the box there are 2 balls and she chose one at random, then she had a 0.5 probability of chose each ball, and then she has a 0.5 probability of choosing the ball that is associated to the correct answer, then she has a 0.5 of getting each answer correct.

Now she has 4 questions, then the probability for getting all of them correct is the product of the probabilities for each one; this is:

0.5*0.5*0.5*0.5 = 0.0625

multiplied by 100%, we get a 6.25% of getting the four answers correct using this method.