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Home / Assignment Help / 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?

# 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?

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. 