probability

Question

A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 40% of the questions correct. (Round your answer to three decimal places.)

Answer 1

Amy, as a former resident of Northridge, I can only hope you're kidding.

40% would be passing?

 

This is an instance of Binomial Probability and can be answered by examining the binomial expansion of (T+F)¹⁰

where T = F = 0.5.

 

You can expand and get eleven terms. The coefficients will be from the "10 row" of Pascal's triangle.

The terms for getting only 3 or less correct are:

T⁰F¹⁰ + 10C1•T•F⁹ + 10C2•T²•F⁸ + 10C3•T³•F⁷

and you can compute the above and call it Z (it's the cumulative probability of failing by only getting 0 through 3 correct).

 

The probability of passing P(>40%) = 1-Z.

 

By the way: in the expression for Z, each term has a common factor (½)¹⁰ so that should be factored out of the expression and all you need is the sum of the first four binomial coefficients from Pascal's triangle, divided by 2¹⁰