5 letters are typed, with repetition allowed. What is the probability that all 5 will be vowels? Write your answer as a percent. Round to the nearest hundredth of a percent as needed
How many letters are there in the alphabet? 26
How many vowels are there in the alphabet? 5
Therefore, the probability of picking one vowel is 5/26.
The probability of picking N vowels is (5/26)^N or 5/26 * 5/26 * 5/26.... (N times).
So for your question, the answer is (5/26)^5 = 0.03% when rounded to the nearest hundredth of a percent.
To find the probability that all 5 letters will be vowels, we need to determine the number of ways we can choose 5 vowels from the set of 5 letters.
There are 5 vowels in the English alphabet: A, E, I, O, and U. Since repetition is allowed, all 5 letters can be chosen from this set.
The total number of ways we can choose 5 letters with repetition allowed is 5^5 since we have 5 choices for each letter.
To find the probability, we need to divide the number of favorable outcomes (choosing all 5 vowels) by the total number of possible outcomes.
Since there is only 1 way to choose all 5 vowels, the number of favorable outcomes is 1.
So, the probability is 1/5^5 = 1/3125.
To express this as a percent, we multiply the probability by 100:
(1/3125) * 100 ≈ 0.032%.
Therefore, the probability that all 5 letters will be vowels is approximately 0.032%.
To find the probability that all 5 letters will be vowels, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. Since repetition is allowed and there are 5 slots to fill, each slot can be filled with any of the 5 vowels (a, e, i, o, u), resulting in 5 options for each slot. Therefore, the total number of possible outcomes is 5^5 = 3125.
Next, let's determine the number of favorable outcomes. In this case, we want all 5 letters to be vowels, which means that each slot needs to be filled with one of the 5 vowels (a, e, i, o, u). There is only 1 set of vowels that satisfies this condition.
Therefore, the number of favorable outcomes is 1.
Finally, we can calculate the probability using the formula:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 1 / 3125 ≈ 0.00032
To express this as a percentage, we multiply the probability by 100 and round to the nearest hundredth of a percent:
Probability ≈ 0.032%
Therefore, the probability that all 5 letters will be vowels is approximately 0.032%.
Well, let's see. There are 26 letters in the English alphabet, and 5 of those are vowels. So, the probability of randomly choosing a vowel for any given letter is 5/26. Since repetition is allowed, we can use this probability for all 5 letters.
To calculate the probability that all 5 letters will be vowels, we simply multiply the probabilities together:
(5/26) * (5/26) * (5/26) * (5/26) * (5/26) = 0.000457...
To convert this into a percentage, we multiply by 100:
0.000457... * 100 = 0.0457...
Rounding to the nearest hundredth, we get approximately 0.05%.
So, the probability that all 5 letters will be vowels is about 0.05%.