A bag contains tiles with the letters A-R-I-T-H-M-E-T-I-C. Amelia chooses a tile without looking and doesn’t replace it. She chooses a second tile without looking. What is the probability that she will choose the letter I both times?
•1/25
•1/45***
•2/45
•2/55
So the prob of picking I the first time = 2/10 = 1/5
You are now returning it, so wouldn't the second draw have the same probability, since the letters certainly don't remember what happened to them ??
So what do you think?
I misread the part about replacing it
I read it as being replaced, so
it should be
(2/10)(1/9) = 1/45
you are right
To find the probability that Amelia will choose the letter I both times, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of letters in the bag, which is 11.
When Amelia chooses the first tile, there are 11 letters in the bag, and 1 of them is the letter I.
After Amelia chooses the first tile, there are now 10 letters in the bag, and 1 of them is the letter I.
Therefore, the number of favorable outcomes is 1 time 1, which is 1.
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 11 times 10
Probability = 1 / 110
Therefore, the correct answer is 1/110, which is not listed among the options provided.
To find the probability that Amelia will choose the letter I for both tiles, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
Amelia chooses one tile without replacement, so the total number of outcomes for the first tile is 14 (as there are 14 letters in total).
For the second tile, since one tile has already been chosen and not replaced, there are now 13 tiles remaining.
The total number of outcomes is therefore 14 * 13 = 182.
Number of Favorable Outcomes:
Amelia needs to choose the letter I for both tiles. There is only 1 tile with the letter I initially, and since there is no replacement, there is still only 1 tile with the letter I for the second draw.
Therefore, the number of favorable outcomes is 1 * 1 = 1.
Probability:
To find the probability, we divide the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
= 1 / 182
Simplifying the fraction, we get:
Probability = 1/182
Therefore, the correct answer is 1/182.