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

Step-by-step explanation:

Given: Total choices to each question = 4

So, the probability that an answer is correct = $\dfrac{1}{4}=0.25$

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