ALLY HAD A GAME WITH 2 GROUPS OF PLAYING TILES. THE FIRST GROUP OF 24 TILES HAD ALL THE LETTERS OF THE ALPHABET EXCEPT U AND Y. EACH TILE HAD 1 LETTER ON IT. THE SECOND GROUP OF 5 TILES HAD THE NUMBERS 1 THROUGH 5, WITH 1 NUMBER ON EACH TILE. IF ALLY DREW 1 LETTER TILE AND 1 NUMBER TILE AT RANDOM. WHAT IS THE PROBABILITY THAT SHE WOULD DRAW A LETTER IN HER NAME AND AN EVEN NUMBER?
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Two of her letters in her name are found in the 24 letter group, and there are 2 evens in the group of number tiles
prob(a letter in her name and an even)
= (2/25)(2/5)
= 4/125
To determine the probability of Ally drawing a letter in her name and an even number, we need to calculate the total number of possible outcomes and the number of desired outcomes.
First, let's calculate the total number of possible outcomes.
Since there are 24 tiles with letters (excluding U and Y), and 5 tiles with numbers, the total number of possible outcomes can be found by multiplying the number of options for each group:
Total possible outcomes = number of letter tiles x number of number tiles
= 24 x 5
= 120
Now, let's calculate the number of desired outcomes, i.e., the number of ways Ally can draw a letter in her name and an even number.
The letters in Ally's name are A, L, and Y. Since there are 24 letter tiles, the probability of drawing an "A" tile is 1 out of 24, the probability of drawing an "L" tile is also 1 out of 24, and the probability of drawing a "Y" tile is 1 out of 24.
The even numbers are 2 and 4. Since there are 5 number tiles, the probability of drawing a "2" tile is 1 out of 5, and the probability of drawing a "4" tile is also 1 out of 5.
Since Ally needs to draw one letter from her name and one even number, the total number of desired outcomes can be found by multiplying the number of options for each category:
Number of desired outcomes = number of letter tiles in her name x number of even number tiles
= (1 out of 24) x (1 out of 5)
= 1/24 x 1/5
= 1/120
Finally, we can calculate the probability by dividing the number of desired outcomes by the total number of possible outcomes:
Probability = number of desired outcomes / total possible outcomes
= (1/120) / (120/120)
= 1/120
Therefore, the probability that Ally would draw a letter in her name and an even number is 1 out of 120.