Question

Cassie cannot remember the correct order of the six letters in her password (which is not case sensitive). She does recall that she used the first six letters of the alphabet. The probability that the first 4 letters of the password are consonants is?

Answer 1

This isn't terribly important (well, actually it is) but you have to note that each of the letters in the password are 'independent' events, meaning, they don't affect each other, such that, if you want the chance that all events happen, you can just multiply them...

Answer 2

Let's look at the first letter... what are the chances that it's a consonant?

Remember that probability is just the number of desired outcomes divided by the total number of outcomes...

Answer 3

4 consonants divide by total six letters for the first slot

Answer 4

yup, so that makes 2/3 right?

Answer 5

Wait, are repetitions allowed? D:

Answer 6

Okay what I just did was 4/6 * 3/5 * 2/4 * 1/3 = 1/15. Which is the answer in the question. However I am not a hundred percent sure on the reasoning behind this

Answer 7

Ahh, I see :P
Then why did you do it, lol :3

Answer 8

It means repetitions aren't allowed...
So, for the first letter, you have 4 consonants out of 6, correct?

Answer 9

Yes. Then for the next slot there are 5 slots and three consonants etc.

Answer 10

5 letters left you mean :3
Because you already took away one (for the first letter)
So 3/5
And it goes on :P

Answer 11

Thanks. So basically it is probability of consonant on the first slot x on 2nd x on 3rd x on 4th. Thus we don't need to add the last two slots probabilities

Answer 12

mhmm :)
Mostly because there'd be no consonants left :P

Answer 13

lol just kidding... yeah, the question is just interested in the first four slots...