The word "independent" is spelled out on index cards, one letter
per card. Ken randomly selects a card and does not replace it,
and then Barb randomly selects a card. What is the probability
that they both get a card with an "e" written on it?

Question

The word "independent" is spelled out on index cards, one letter 
per card. Ken randomly selects a card and does not replace it, 
and then Barb randomly selects a card. What is the probability 
that they both get a card with an "e" written on it?

anonymous · Answer

The word independent consists of 11 letters, of which 3 are e's, these are the three e's you want at your first pick, let it be Ken. Now for Barb, one card is gone, in favor for this problem it will be the e, there are only 2 e's left and a total of 10 cards.

anonymous · Answer

so what would that be ? 1/16

anonymous · Answer

I ended up with 3/55

anonymous · Answer

boo thats not one of my options =/

anonymous · Answer

can you write me down your options please?

anonymous · Answer

1/169 , 1/2 , 1/16

anonymous · Answer

Sorry then, I can't cope with these answers, the 1/16 is very near to mine, but I don't see how they would achieve such a result.

anonymous · Answer

huh. okay, well thanks for you help! (: ill look into further.

anonymous · Answer

I N D E P E N D E N T, 11 Characters, 3 E's

If you write 1 letter per card, you have 11 cards a total. Now no matter how you turn it, you pick one card, the probability is given by relative weight of the letter, like you can pick an I, but there is only one I, so your probability to pick that exactly one 1 is 1/11.

Same logic applies for the e's, there are 3 of them. So your probability to pick one E out of 11 Cards (from which 3 are E written on) is 3/11.

Same conditions should apply for the second player, just that one E is gone and therefore one card less, meaning 2 E's and 10 cards. His probability to pick a card with the letter E on it is 2/10

anonymous · Answer

i see what youre getting at, i just sent an email to my teacher, cause that isnt the first time it has happened to me. =/

anonymous · Answer

Maybe somebody else like @Zarkon can double check my logic, the hour here is pretty advanced. But I just can't think of any reasonable way (yet) how to get at the answer options they gave you.

zarkon · Answer

I get the same answer as you

anonymous · Answer

Thank you, got me scratching my head for a while.

zarkon · Answer

there must be a typo in the question or answers

anonymous · Answer

I agree.

anonymous · Answer

well, theres four answers but two are 1/169 so im thinking thats where they messed up, i asked cause i knew none of those seemed right.