Use counting rules to determine the probability.
-A student takes a true-false test consisting of 12 questions. Assuming that the student guesses at each question, find the probability that the student answers exactly 10 questions correctly.
A)0.0129
B)0.0161
C)0.0097
D)0.0064

Question

Use counting rules to determine the probability.
-A student takes a true-false test consisting of 12 questions. Assuming that the student guesses at each question, find the probability that the student answers exactly 10 questions correctly. 
A)0.0129
B)0.0161
C)0.0097
D)0.0064

Quizplus · Accepted Answer

The probability of guessing exactly 10 out of 12 questions correctly on a true-false test can be calculated using the binomial probability formula, which is P(X=k) = (nCk) * p^k * (1-p)^(n-k), where n is the total number of questions, k is the number of correct answers, p is the probability of getting a question right, and (nCk) is the combination of n items taken k at a time. Here, n=12, k=10, and p=0.5 (since it's a true/false test). Thus, P(10 correct out of 12) = (12C10) * (0.5)^10 * (0.5)^2 = 66 * (0.5)^12 = 0.0161.

Use Counting Rules to Determine the Probability