Question #e7870

1 Answer
Jan 12, 2018

#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#