Astudy conducted on 40,000 words in the english language found that about 6,670 words started with the letter t, which is the most common letter to start a word. if we randomly pick 20 unique words, which of these lists of words will come closest to the theoretical probability of getting a word beginning with t?

Hi so your total samples are 40000 and 6670 start with T, so if we pick a random word of that 40000 we will have a 6670/40000 = 0.167 (or 16.7%) probability of picking one that starts with T.

So if i pick a list with 20 unique words and i want that have  the closest possible probability of getting a word starting with T as the one i had before, then:

if x are the total of words that start with t in our sample of 20 words.

then x/20 = 0.167 so x= 0.167*20 = 3.34

So the list with the closest possibility will be the list that has 3 words that start with T.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: