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?(1 point) Responses 412.412 Start Fraction 4 over 12 End Fraction times Start Fraction 4 over 12 End Fraction 48. 48 Start Fraction 4 over 8 End Fraction times Start Fraction 4 over 8 End Fraction 412+412 Start Fraction 4 over 12 End Fraction plus Start Fraction 4 over 12 End Fraction 312.211
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The correct answer is 48 Start Fraction 4 over 8 End Fraction times Start Fraction 4 over 8 End Fraction.
To find the probability of drawing two Ns with replacement, we need to figure out the probability of drawing an N on the first draw and an N on the second draw.
There are a total of 8 letters in the box (B N T P N N T P B). Out of those 8 letters, 4 of them are Ns.
On the first draw, the probability of drawing an N is 4 out of 8, or Start Fraction 4 over 8 End Fraction.
Since the first letter is replaced, the number of Ns and total letters remain the same for the second draw.
Therefore, the probability of drawing another N on the second draw is also Start Fraction 4 over 8 End Fraction.
To find the probability of both events happening (drawing an N on the first draw and an N on the second draw), we multiply the individual probabilities: Start Fraction 4 over 8 End Fraction times Start Fraction 4 over 8 End Fraction.
This gives us a final probability of 48 Start Fraction 4 over 8 End Fraction times Start Fraction 4 over 8 End Fraction.