SOLUTION: A student is taking a​ multiple-choice exam in which each question has five choices. Assuming that she has no knowledge of the correct answers to any of the​ questions,

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Question 1086300: A student is taking a​ multiple-choice exam in which each question has five 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 five balls 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 six multiple-choice questions on the exam. Complete parts​ (a) through​ (d) below.
a. What is the probability that she will get six questions​ correct?
​(Round to four decimal places as​ needed.)
b. What is the probability that she will get at least five questions​ correct?
​(Round to four decimal places as​ needed.)
c. What is the probability that she will get no questions​ correct?
​(Round to four decimal places as​ needed.)
d. What is the probability that she will get no more than two questions​ correct?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the probability that she will get the answer to any one of the questions correctly is 1/5 because there are 5 balls and only one of the balls will determine the correct answer each time.

p = 1/5 = .2
q = 1 minus p = 4/5 = .8

p(x) = p^x * q^(n-x) * c(n,x)

p is the probability that the question will be answered correctly.
q is the probability that the question will not be answered correctly.
n is the number of questions to be answered.
c(n,x) is the number of possible ways to get sets of x elements out of a set of n elements without order of the elements in the set being a consideration.

the probabilities for x from 0 to 6 are shown below:

$$$

your questions with answers are shown below.

answers are in the spreadsheet as well.

you can round them as required.

a. What is the probability that she will get six questions​ correct?

this is equal to p(6) which is equal to 0.000064

b. What is the probability that she will get at least five questions​ correct?

this is equal to p(5) + p(6) which is equal to 0.001536 + 0.000064 which is equal to 0.0016

c. What is the probability that she will get no questions​ correct?

this is equal to p(0) which is equal to 0.262144

d. What is the probability that she will get no more than two questions​ correct?

this is equal to p(0) + p(1) + p(2) which is equal to .262144 + .393216 + .24576 which is equal to .901120

the sum of all probabilities is equal to 1 as it should always be.