A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions...?

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions...?
this is the probability of getting 7 success out of ten when the prob of success = prob of failure = 1/2





use the binomial probability:





Prob of 7 successes out of 10 = 10!/[7!3!] (1/2)^10





=120/1024=11.72%





not highly likelyA test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions...?
The tricky thing is to consider that you can get 7 questions right, 8 questions right, 9 questions right or 10 questions right. You need to add up all these probabilities (not just 7 like another answerer did).





There are 1024 ways to answer the questions 2^10 = 1024 ways.





There are 10C7 ways to get 7 out of 10 correct.


10C7 = 10 x 9 x 8 / 3! = 120 ways





There are 10C8 ways to get 8 out of 10 correct


10C8 = 10 x 9 / 2! = 45 ways





There are 10C9 ways to get 9 out of 10 correct


10C9 = 10 / 1! = 10 ways





There are 10C10 ways to get 10 out 10 correct


10C10 = 1 way





120 + 45 + 10 + 1 = 176 good outcomes out of 1024 possible outcomes.





176 / 1024 = 0.171875





Answer:


Approx. 17.2%



If the student must get 7 questions correct and they have a 50% chance of getting one question right, you must multiply .5 seven times


(.5^7). The student has 0.78125% chance of passing the test.
he wont