Question

4 letters are typed, without repetition. What is the probability that all 4 will be vowels? Write your answer as a percent. Round your answer to three decimal places

Answer 1

To find the probability that all 4 letters will be vowels, we need to consider the total number of possible outcomes and the number of favorable outcomes. The probability is approximately 0.006 or 0.6%.

Step-by-step explanation:

To find the probability that all 4 letters will be vowels, we need to consider the total number of possible outcomes and the number of favorable outcomes.

The total number of ways to choose 4 letters from the set of 26 letters of the alphabet (assuming we have a letter set that includes all the letters of the alphabet) is given by the combinations formula: C(26, 4) = 26! / (4!(26 - 4)!)

Now, the number of favorable outcomes is the number of ways to choose 4 letters from the set of vowels (a, e, i, o, u): C(5, 4) = 5! / (4!(5 - 4)!)

The probability is then given by the ratio of the number of favorable outcomes to the total number of outcomes: P = C(5, 4) / C(26, 4)

Using a calculator, we can find P to be approximately 0.006 or 0.6%.

Answer 2

2/13; 15.38%; 0.154

Step-by-step explanation:

Since total number of letters in the alphabet is equal to 26, this will give the total outcome.

If 4 letters are typed, without repetition, the expected outcome is 4 since there are no repetition.

Probability = expected number of outcome/total number of outcome

Probability that all 4 will be vowels will be;

P(all vowels) = 4/26 = 2/13

Expressing 2/13 as percent, we will have;

2/13 × 100

= 200/13

= 15.38%

Expressing 2/13 as decimal will give;

2/13 = 0.1538

2/13 = 0.154( to 3 decimal places)

Note that the third digits after the decimal point 3 is rounded off to 4 because the number succeeding it is 8 which greater than 4