# Video: Determining the Probability of the Intersection of Two Independent Events

One letter is randomly selected from the word EVEN, and another is randomly selected from the word LETTER. What is the probability that both letters are vowels?

01:38

### Video Transcript

One letter is randomly selected from the word EVEN, and another is randomly selected from the word LETTER. What is the probability that both letters are vowels?

In this question, we have two events taking place: the selection of a letter from the word EVEN and the selection of a letter from the word LETTER. We’re looking for the probability that both of these letters are vowels or the intersection of these two independent events.

Remember these events are independent because the outcome of one doesn’t affect the outcome of the other. The key rule we need is that if two events 𝐴 and 𝐵 are independent, then the probability of the intersection, 𝐴 and 𝐵, can be found by multiplying the individual probabilities together.

So let’s start by finding the individual probabilities of selecting a vowel from each of the two words. The word EVEN has two vowels and four letters in total, so the probability of selecting a vowel is two out of four, which simplifies to a half.

The word LETTER also has two vowels, but six letters in total, so the probability of selecting a vowel is two out of six, which simplifies to a third.

Finally to find the probability that both letters are vowels, we multiply these two probabilities together, one-half multiplied by one-third. And therefore we have an answer to the problem: the probability that both letters are vowels is one-sixth.