Question

Let’s say that using the six letters of the word BRAISE, you formed all possible four-letter words. You wrote each of these words on a separate piece of paper and put them all in a bag. Now, you pick a paper randomly from the bag. What is the probability that the word on that paper would start with the letter B?

Answer 1

Answer: 1/6

Explanation:

To find the probability that the word on the randomly chosen paper starts with the letter B, you need to determine how many four-letter words can be formed from the six letters in BRAISE, and then calculate the probability that one of those words starts with B.

First, let's count the total number of four-letter words that can be formed from the letters in BRAISE. Since you have six letters to choose from for each of the four positions, the total number of four-letter words is 6^4 (6 choices for the first letter, 6 choices for the second letter, and so on).

Now, let's count the number of four-letter words that start with the letter B. In this case, you have fixed the first letter as B, so there are no choices for the first letter. For the remaining three positions, you still have 6 choices for each. So, there are 6^3 four-letter words that start with B.

To find the probability, divide the number of four-letter words that start with B by the total number of four-letter words:

Probability = (Number of words that start with B) / (Total number of four-letter words)

Probability = (6^3) / (6^4)

Probability = (6 * 6 * 6) / (6 * 6 * 6 * 6)

Probability = (216) / (1296)

Now, simplify the fraction:

Probability = 1/6

So, the probability that the word on the randomly chosen paper starts with the letter B is 1/6.