Question

A multiple-choice examination has 10 questions, each with four possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least six questions correctly?​

Answer 1

`0.0197277`

Explanation:

Consider the random variable X

Where X denotes the number of (success/having a correct answer)

in 10 identical and independent trials .

then

X follows the Binomial distribution with parameters

10 and p = p(success) = 1/4

`p\left( X\geq 6\right) =\sum^(10)_(k=6) p\left( X=k\right)`

`=\sum^(10)_(k=6) C^(k)_(10)\left( (1)/(4) \right)^(k) \left( (3)/(4) \right)^(10-k)`

`=(20686)/(2^(20)) \\= 0.0197277`