i have some algebra questions please fill all blanks thank y

i have some algebra questions. please fill all blanks thank you

A test contains 10 multiple choice questions, each with four possible answers. If a student was to simply guess what the answers are, then we can model the final number of questions this student gets correct as a binomial distribution B(n, p) with n = and p = If the pass mark is 5 out of 10, what is the probability that this student will pass the test? It is (to 5 decimal places) What is the probability the student gets at most 2 out of 10? It is (to 5 decimal places)

Solution

1)p = propability of choosing correct option out of 4 =1/4

We have 10 questions , so n will be 10 for B(n,p)

2)as passing marks is 5, so probability of getting 5 correct answers out of 10 is

= (1/4)⁵ *(3/4)⁵

= 0.00023174285

2)atmost 2 out of 10 = 0 correct + 1 correct + 2 correct

= (3/4)¹⁰ + (1/4)(3/4)⁹ +(1/4)²(3/4)⁸

⁼(3¹⁰ + 3⁹ + 3⁸)/4¹⁰

=0.08134