Question

Probability Question: A student is taking a multiple choice question. Each question has 4 choices. There are 20 question in the test and the student answers them all randomly. Determine the probability that the student has at least 10 correct answers. Answer to 4 decimal places

Answer 1

Answer: 0.9961

Explanation:

Given: Total choices to each question = 4

So, the probability that an answer is correct =
`(1)/(4)=0.25`

Total questions = 20

i.e. n= 20

Let x be the binomial variable that represents the number of correct answers.

So, the probability that the student has at least 10 correct answers.

`B(x=10;n=20, p=0.25)=\sum\limits_(i=0)^(x)(i;n=20,p=0.25)`

`=0.9961` [By using cumulative binomial table]

Hence, the probability that the student has at least 10 correct answers = 0.9961