Question

A student takes a 10 multiple choice test by guessing. Each question has 4 choices use the binomial distribution to compute the student gets at least 7 correct

Answer 1

WE have 10 questions, the answer is either right or wrong whatever the number of choices. Then P(right) = 1/2 and Q(wrong) =1/2
Moreover as per the given of the problem, he may get at least 7 right answers, that means he can get 7 OR 8 OR 9 OR 10 right answers:
Here-below the binomial probability distribution:

 a) for 7 exactly right answers : ¹⁰C₇ (1/2)⁷(1/2)³     =  0.117187

b) for 8 exactly right answers : ¹⁰C₈ (1/2)⁸(1/2)²      =  0.043945

c) for 9 exactly right answers : ¹⁰C₉ (1/2)⁹(1/2)¹      =  0.009656

d) for 10 exactly right answers : ¹⁰C₁₀ (1/2)¹⁰(1/2)⁰  = 0.000488
                                                                                  -------------
                                                  Σ (PROBABILITY) =  0.171276

P( 7 or 8 or 9 or 10) = 0.1712 OR 17.12%