consider a bowl containing 36 different slips of paper. Ten of the slips of paper each contain one of the set of digits 0 through 9 and 26 slips each contain one of the 26 letters of
the alphabet. Determine the probabilities of the events specified.
Drawing one slip, what is P(even number or a vowel)?
I know that there are four even numbers and five vowels. How do I figure this out?
so that would make it simply as
9/36 or 1/4
To determine the probability of drawing either an even number or a vowel from the bowl, you need to find the ratio of the number of favorable outcomes (slips with even numbers or vowels) to the total number of possible outcomes (all 36 slips).
To calculate this probability, follow these steps:
Step 1: Count the number of favorable outcomes:
- There are four even numbers: 0, 2, 4, and 6.
- There are five vowels: A, E, I, O, and U.
Therefore, the number of favorable outcomes is 4 (even numbers) + 5 (vowels) = 9.
Step 2: Count the total number of possible outcomes:
- There are 10 slips with digits (0-9).
- There are 26 slips with letters (A-Z).
Therefore, the total number of possible outcomes is 10 (digits) + 26 (letters) = 36.
Step 3: Calculate the probability:
- P(even number or vowel) = Number of favorable outcomes / Total number of possible outcomes = 9/36.
Simplify this fraction by dividing the numerator and denominator by their greatest common divisor (GCD):
- GCD(9, 36) = 9
- 9/9 = 1
- 36/9 = 4
So, the simplified probability is:
- P(even number or vowel) = 1/4 or 0.25
Therefore, the probability of drawing either an even number or a vowel from the bowl is 1/4 or 0.25.