Find the indicated probability. round to three decimal places. a test consists of 10

a. True

b. False questions. to pass the test a student must answer at least 6 questions correctly. if a student guesses on each question, what is the probability that the student will pass the test?

To answer this problem, we use the binomial distribution formula for probability:

P (x) = [n! / (n-x) ! x!] p^x q^ (n-x)

Where,

n = the total number of test questions = 10

x = the total number of test questions to pass = >6

p = probability of success = 0.5

q = probability of failure = 0.5

Given the formula, let us calculate for the probabilities that the student will get at least 6 correct questions by guessing.

P (6) = [10! / (4) ! 6!] (0.5) ^6 0.5^ (4) = 0.205078

P (7) = [10! / (3) ! 7!] (0.5) ^7 0.5^ (3) = 0.117188

P (8) = [10! / (2) ! 8!] (0.5) ^8 0.5^ (2) = 0.043945

P (9) = [10! / (1) ! 9!] (0.5) ^9 0.5^ (1) = 0.009766

P (10) = [10! / (0) ! 10!] (0.5) ^10 0.5^ (0) = 0.000977

Total Probability = 0.376953 = 0.38 = 38%

There is a 38% chance the student will pass.