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 Ns if the first letter is replaced before drawing the second?

Answer 1

To find the probability of drawing two Ns with replacement, we need to determine the probability of drawing an N on the first draw, and then multiply it by the probability of drawing an N on the second draw.

The probability of drawing an N on the first draw is calculated by dividing the number of Ns in the box by the total number of letters in the box. In this case, there are 4 Ns and 12 total letters, so the probability of drawing an N on the first draw is 4/12.

Since the first letter is replaced before the second draw, the probability of drawing an N on the second draw is also 4/12.

To find the probability of both events occurring (drawing an N on the first draw and an N on the second draw), we multiply their probabilities together:

(4/12) * (4/12) = 16/144

Simplifying the fraction, we get:

16/144 = 1/9

Therefore, the probability of drawing two Ns with replacement is 1/9.