A Test Consists Of 10​ True/false Questions. To Pass The Test A Student Must Answer

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A test consists of 10 true/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?

Round to three decimal places.

  • A. 0.205
  • B. 0.172
  • C. 0.828
  • D. 0.377

Answer

There is an equal chance of getting n on the test as getting 10-n on the test: just rename correct to incorrect.

The choices of answers for each question =2

Then, the probability of choosing a correct option: p= 0.5

Total number of question: n=10

Also, to pass the test, a student must correctly answer at least 6 questions.

Let x be the random variable that represents the number of questions answered.

(10 choose 5) sequence of 10 trues or falses have 5 trues  2a + the chance of getting 5 = 1.  (1-((10choose5)/(2^10)))/2=a =  (1–252/1024)/2=a  a= 386/1024=193/512 Which is around 37.695%

Answer: There is a 0.377 chance that the student will pass the test.

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