SOLUTION: I need assistance with this homework: A test consists of 10 true-or-false questions. An answer is randomly chosen for each question. What is the probability of answering exact

Algebra ->  Probability-and-statistics -> SOLUTION: I need assistance with this homework: A test consists of 10 true-or-false questions. An answer is randomly chosen for each question. What is the probability of answering exact      Log On


   



Question 429565: I need assistance with this homework:
A test consists of 10 true-or-false questions. An answer is randomly chosen for each question.
What is the probability of answering exactly 4 questions correctly? Answer in fraction.
What is the probability of answering at least 2 questions correctly? Answer in fraction.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Note: The probability of x successes in n trials is:
P = nCx* p%5Ex%2Aq%5E%28n-x%29 where p and q are the probabilities of success and failure respectively.
In this case p & q are = 1/2 or .5
nCx = n%21%2F%28x%21%28n-x%29%21%29
10 true/false questions:
P(answering exactly 4 correct)= 10C4(.5)^4(.5)^6 = 210(.5)^4(.5)^6
P(of answering at least 2 questions correctly) = 1 -P(none) -P(one)
1 - (.5)^10 - 10(.5)(.5)^9