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?
A. start fraction 1 over 25 end fraction
B. Start Fraction 1 over 45 End Fraction
C. start fraction 2 over 45 end fraction
D. start fraction 2 over 55 end fraction
There are a total of 11 tiles with the letter I out of 12 tiles in total. After Amelia chooses one tile without replacement, there are only 10 tiles left and only 1 with the letter I. The probability of choosing the letter I on the second pick is therefore 1/10. The probability of choosing the letter I both times is the product of those probabilities: 11/12 x 1/10 = 11/120. This reduces to Start Fraction 11 over 120 End Fraction, which is answer choice D.
A sandwich shop offers the following toppings. How many two-topping sandwiches can you make?
lettuce
tomato
bacon
cheese
mustard
A. 8
B. 10
C. 12
D. 20
To count the number of two-topping sandwiches, we need to use the combination formula:
n choose k = n! / (k!*(n-k)!)
where n is the total number of items and k is the number of items we want to choose.
In this case, we have 5 toppings and we want to choose 2, so:
5 choose 2 = 5! / (2!*(5-2)!) = 10
Therefore, there are 10 two-topping sandwiches that can be made. The answer is B.
Alli's ice cream shop offers 5 flavors and 10 toppings. Jali's ice cream shop offers 7 flavors and 7 toppings. Fernando's ice cream shop offers 9 flavors and 6 toppings. Laura's ice cream shop offers 13 flavors and 4 toppings.
If you want one flavor of ice cream and one topping, which shop gives you the most options?
A. Alli's ice cream shop
B. Jali's ice cream shop
C. Fernando's ice cream shop
D. Laura's ice cream shop
To calculate the number of options for one flavor of ice cream and one topping, we need to multiply the number of flavors by the number of toppings for each shop, and then compare the results.
For Alli's ice cream shop: 5 x 10 = 50 options
For Jali's ice cream shop: 7 x 7 = 49 options
For Fernando's ice cream shop: 9 x 6 = 54 options
For Laura's ice cream shop: 13 x 4 = 52 options
Therefore, the ice cream shop with the most options for one flavor of ice cream and one topping is Fernando's, with 54 options. The answer is C.
To find the probability of choosing the letter "I" both times, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
Since Amelia chooses without replacement, the total number of outcomes for the first choice is 15 (all 15 letters in the bag). For the second choice, after one letter has been removed, the total number of outcomes is 14.
Favorable Outcomes:
The first choice doesn't affect the second choice's probability, so regardless of what letter Amelia chooses first, there are still 2 "I" tiles left in the bag. Therefore, the number of favorable outcomes is 2.
Now we can calculate the probability:
Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes)
Probability = 2/15 * 2/14
Simplifying, we get:
Probability = 4/210
Therefore, the correct answer is D. Start fraction 2 over 55 End fraction.
To find the probability that Amelia will choose the letter "I" both times, we need to count the number of favorable outcomes and the total number of possible outcomes.
The bag contains 13 letters, including 2 "I" tiles. After Amelia chooses a tile without looking, there will be one less tile in the bag. Therefore, the total number of possible outcomes for the second pick will be reduced by 1.
So, the total number of possible outcomes for choosing a tile without replacement is 13 for the first pick and 12 for the second pick.
Now, let's count the number of favorable outcomes, which is the number of ways Amelia can choose the letter "I" both times. Since there are 2 "I" tiles, Amelia can choose the first "I" tile in 2 ways and the second "I" tile in 1 way.
Therefore, the number of favorable outcomes is 2.
So, the probability of choosing the letter "I" both times is favorable outcomes over total outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 2 / (13 × 12)
= 2 / 156
= 1 / 78
Now, let's find the given options:
A. 1/25
B. 1/45
C. 2/45
D. 2/55
Comparing the probability we calculated (1/78) with the given options, we see that none of the options match the calculated probability.
Therefore, none of the given options is the correct answer.