Teresa put tiles marked with the letters of her name into a bag. The back of each tile is blank.
The tiles are shown below.
T
E
R
E
S
A
Without looking into the bag, Teresa will pick a tile.
a. What is the probability that Teresa will pick a tile with the letter T on it? Show or explain
how you got your answer.
b. What is the probability that Teresa will pick a tile with a vowel (A, E, I, O, U) on it?
Show or explain how you got your answer.
Suppose Teresa first picked a tile with a vowel on it. Now Teresa will pick a second tile.
• She will not put the first tile back into the bag.
• She will not look into the bag while picking the second tile.
c. What is the probability that Teresa will pick another tile with a vowel on it? Show or
explain how you got your answer.
a. Assuming that these are the only tiles in the bag, there are six possibilities. The letter T is only one of these possibilities = 1/6
This should give you an idea of how to do b and c.
a. To find the probability of picking a tile with the letter T on it, we divide the number of tiles with the letter T by the total number of tiles.
Number of tiles with the letter T: 1
Total number of tiles: 6 (since there are 6 different letters)
Therefore, the probability of picking a tile with the letter T on it is 1/6.
b. To find the probability of picking a tile with a vowel on it, we count the number of tiles with vowels (A, E) and divide it by the total number of tiles.
Number of tiles with vowels: 2 (E and A)
Total number of tiles: 6
Therefore, the probability of picking a tile with a vowel on it is 2/6, which simplifies to 1/3.
c. Since Teresa already picked a tile with a vowel on it, there are now 1 fewer tile with vowels and 1 fewer total tile.
Number of remaining tiles with vowels: 1 (A)
Total number of remaining tiles: 5
Therefore, the probability of picking another tile with a vowel on it is 1/5.
a. To find the probability that Teresa will pick a tile with the letter T on it, we need to determine the number of favorable outcomes (tiles with the letter T) and the total number of possible outcomes (total number of tiles).
Favorable outcomes: 1 (there is only one tile with the letter T)
Total outcomes: 6 (there are 6 tiles in total)
Therefore, the probability of picking a tile with the letter T is 1/6.
b. To find the probability that Teresa will pick a tile with a vowel on it, we need to determine the number of favorable outcomes (tiles with the vowels A, E, I, O, and U) and the total number of possible outcomes (total number of tiles).
Favorable outcomes: 2 (there are two tiles with the vowels E and A)
Total outcomes: 6 (there are 6 tiles in total)
Therefore, the probability of picking a tile with a vowel is 2/6 or simplified as 1/3.
c. After Teresa picks a tile with a vowel (let's say she picked the E), there will be one less vowel available in the remaining tiles and one less tile overall. To find the probability of picking another tile with a vowel, we need to determine the new number of favorable outcomes and the new total number of possible outcomes.
New favorable outcomes: 1 (there is only one tile with the vowel A remaining)
New total outcomes: 5 (there are 5 tiles remaining)
Therefore, the probability of picking another tile with a vowel is 1/5.