A student is taking a multiple choice exam which has 6 test

A student is taking a multiple choice exam which has 6 test questions, each of which have 5 options. Assume that the student has no knowledge of the correct answers to any of the questions. She guesses the correct option with a probability of 0.7. what is the probability that

a. she will answer all 6 questions correctly?

b. she will answer at least 4 questions correctly?

c. she will answer none of the questions correctly

? d. she will answer, at most, 3 questions correctly?

Solution

so, the exam has 6 questions and 5 oprions for each of them.
prob. of guessing the correct answer = 0.7 so,the prob. of guessing the wrong answer = 1-0.7 =0.3 a) she will answer all 6 questions correctly = (6 c 6) (0.7)^6 (0.3)^0 = 0.117649

b) she will answer at least 4 ques correctly= ( 6 c 4) (0.7)^4 (0.3)^2 +(6 c 5) (0.7)^5(0.3)^1+(6c6)(0.7)^6 (0.3)^0
=0.74431
c) she will answer none of them correctly = (0.3)^6 =0.000729

d) she will answer at most 3 ques correctly = 1 - p(guessing 4 ques. correctly)-p(guessing 5 ques. correctly)- p(guessing 6 ques. correctly) = 1 - 0.74431 = 0.25569