A box has these letters inside it: B N T P N N T P B B N T. Which answer shows how to find the probability of drawing two And if the first letter is replaced before drawing the second?
To find the probability of drawing two letters, with replacement, from the given box, follow these steps:
1) Determine the total number of letters in the box. In this case, there are 12 letters: B, N, T, P, N, N, T, P, B, B, N, and T.
2) Determine the number of times the first letter appears in the box. Let's say the first letter is B. Count the number of B's in the box, which is 3.
3) Determine the number of letters remaining in the box after the first letter is drawn and replaced. Since there are 12 letters and the first letter is replaced, there are still 12 letters remaining in the box.
4) Determine the number of times the second letter could be any of the letters in the box. Since all 12 letters remain in the box and each letter has an equal probability, any letter can be chosen. Therefore, there are 12 possibilities for the second letter.
5) Multiply the probability of choosing the first letter (step 2) by the probability of choosing the second letter (step 4). The probability of choosing the first letter (B) is 3/12, and the probability of choosing the second letter from the remaining 12 letters is 1/12. Multiplying these probabilities gives:
(3/12) * (1/12) = 1/48
Therefore, the probability of drawing two letters, with replacement, and the first letter being B is 1/48.