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?
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.