Question

Question #e7870

Answer 1

`37/42`

Explanation:

Let's find the opposite outcome: what's the probability that no vowels are chosen?

Well, BREAKDOWN has 9 letters, and 6 are consonants. The probability that the first letter chosen being a consonant is `6//9`.

Now assume we choose a second letter. We have left only 8 letters now, and since we already chose a consonant, only 5 consonants are left. The probability of picking a second consonant is `5//8`.

Using the same logic, the probability of choosing a third consonant is `4//7` and a fourth consonant is `3//6`.

So, the probability of choosing all 4 letters that are all consonants is:

`6/9(5/8)(4/7)(3/6)`

Simplifying...

`=2/3(5/8)(4/7)(1/2)=5/42`

What we want, however, is the case where at least `1` vowel is selected. This has zero overlap with the case we found, where `0` vowels are selected.

Thus, the probability we are looking for is:

`1-5/42=37/42`