Each letter of the alphabet is written on a separate piece of paper and placed in a box. Find the
probability of drawing a vowel, {a, e, i, o, u}, or a letter in the word "segments"?
5 out of 26 for drawing a vowel
Line up the letters of the word segments and the vowels,
s e g m e n t s a e i o u
and remove the duplicates.
The number of unique letters that remain represent the number of successful choices out of 26.
Can you find the probability,
P({s e g m n t}∪{a e i o u})?
I think I have it! Is it 11/26?
Did you remove all the duplicates?
Is the answer 6/13?
6/13 is not correct, becuase it translates to 12/26, meaning that there are 12 possible choices.
If we simplify
{s e g m n t}∪{a e i o u}
={s g m n t a e i o u}
becaue identical members are not shown in duplicate.
So there are 10 possible succesful outcomes out of 26.
What would be the probability of this happening?
5/13
Correct!
To find the probability of drawing a vowel or a letter in the word "segments" from the box, you need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes
To find the number of favorable outcomes, we need to count the number of vowels and the number of letters in the word "segments". Let's break it down:
Number of vowels in the alphabet: There are five vowels in the alphabet: {a, e, i, o, u}.
Number of letters in the word "segments": There are eight letters in the word "segments".
Step 2: Determine the total number of possible outcomes
The total number of possible outcomes is the total number of letters in the alphabet (26) plus the number of letters in the word "segments" (8). This is because you can draw any letter from either the alphabet or the word "segments".
Total number of possible outcomes = 26 + 8 = 34
Step 3: Calculate the probability
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
Number of Favorable Outcomes = Number of vowels + Number of letters in the word "segments"
= 5 + 8
= 13
Probability = 13 / 34
Therefore, the probability of drawing a vowel or a letter in the word "segments" is 13/34, which can also be simplified as approximately 0.382 or about 38.2%.