4 letters are typed, with repetition allowed. What is the probability that all 4 will be vowels? Write your answer as a percent. Round to the nearest hundredth of a percent as needed.
To find the probability of getting all 4 vowels, we first need to determine the total number of possible outcomes.
There are 26 letters in the alphabet, and with repetition allowed, each of the 4 positions can be filled with any of the 26 letters. Therefore, the total number of possible outcomes is 26^4.
Next, we need to determine the number of favorable outcomes, i.e., the number of ways to get all 4 vowels. Since there are 5 vowels in the English alphabet (a, e, i, o, u), each of the 4 positions can be filled with any of the 5 vowels. Therefore, the number of favorable outcomes is 5^4.
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (number of favorable outcomes) / (total number of possible outcomes)
= 5^4 / 26^4
Calculating this, we find:
Probability ≈ 0.0221
To express this as a percentage, we multiply by 100:
Probability ≈ 2.21%
Therefore, the probability of typing 4 letters with repetition allowed, and all 4 being vowels, is approximately 2.21%.
To find the probability that all 4 letters will be vowels, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes: Since repetition is allowed and there are 5 vowels (a, e, i, o, u), there are 5 choices for each of the 4 letters. Thus, there are 5^4 = 625 possible outcomes.
Number of favorable outcomes: Since we want all 4 letters to be vowels, there is only 1 favorable outcome (aaaa, eeee, iiii, oooo, or uuuu).
Therefore, the probability is: 1 favorable outcome / 625 possible outcomes = 1/625.
Converting this to a percentage: (1/625) * 100 ≈ 0.16%.
So, the probability that all 4 letters will be vowels is approximately 0.16%.
In what way does this question differ from your other one?
https://www.jiskha.com/display.cgi?id=1511142923
What simple adjustment do you think you should make?