Question

A student studying for a vocabulary test knows the meanings of 10 words from a list of 26 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows? (Round your answer to three decimal places.)

Answer 1

This is a case of binomial distribution since the event can give only two results( student will know the meaning of the word or he does not). One of them is a success and other is a failure.

The probability of success/failure will remain same in each trial.

We know there are 26 words in a list and the student knows the meaning of 10 words out of them.

Now, if a test contains 10 words from that list, we need to find the probability that at least 8 of the words on the test are words that the student knows.

Let's say success here is that the student knows the word.

So the probability of success is 10/26

hence probability of failure is 1-10/26 = 16/26

Let X be the random variable that denotes the number of words that student knows. Therefore,

where

p is the probability of success

q is the probability of failure

n is the sample size (here number of words from the list that is 10)

We need to find,

= 0.009