Question

You are playing a solitaire game in which you are dealt three cards without replacement from a simplified deck of 10 cards (marked 1 through 10) . You win if one of your cards is a 10 or if all of your cards are odd. How many winning cards are there if different orders are different hands? what is your chance of winning?

Answer 1

5*4*3 + 9*8

Answer 2

\[P(win) = \frac{132}{720}\]

Answer 3

how did you get the 9*8 term?

Answer 4

10 is a must - then 9 free-choices and that leaves 8 free choices

Answer 5

Soo WHAT ?

Answer 6

OK you are new - the custom here on this site is , that when problem is solved
the asker clicks the blue button "best response" to the one who solved it

Answer 7

So, I'm still trying to understand the "must" part, and it wasn't my original question... I like your answer, just trying to understand it.

Answer 8

\[ \color{fuchsia}{\text{if one of your cards is a 10 }} \]

Answer 9

you start there because that's the definition of a win?

Answer 10

One of the two definitions

Answer 11

Btw @aromaboss what about a medal ?

Answer 12

so, with probability of win = # of winning possibilities vs. total possible hands, you say "if I have won, I must have a 10, and given that I have a 10, I have 9*8 ways to choose my remaining 2 cards since they don't matter", so for the "at least one 10" winner, there are 72 possible winning hands, and 720 total hands?

Thanks... not sure why I wasn't getting that at first.

I'll give you a medal just for chatting... bad form for aromaboss though... :(

Answer 13

@JakeV8 human morality is in fact an instrument of fitting into society of peers. See !

Answer 14

much better :)

Answer 15

so chances of winning is 132/170 ? any explanation how you reached this answer?
whats the answer for "how many winning hands are there if different orders are different hands?

Answer 16

Semper Fidelis

Answer 17

am not sure how to give or click medal..guide me.. am new here

Answer 18

5*4*3 + 9*8 =
5 first odd*4second odd*3third odd + OR (9 choices when 10 you have)*(8 choices for the second NON-ten)

Answer 19

720 = 10 first card*9 second card*8third card

Answer 20

@aromaboss... you might have already done it... if not, click the "best response" thing beside on of @Mikael's responses.

Answer 21

thanks mike i will click

Answer 22

thank you jake

Answer 23

CHANCES OF WINNING ANSWER AM NOT CLEAR
HOW MANY WINNING HANDS ARE THERE IF DIFFERENT ORDER ARE DIFFERENT HANDS.
PLEASE HELP ME.

Answer 24

I think you already have this, but maybe you aren't seeing it with all the discussion here...

Answer 25

Total chance of winning = [# of ways to win with odds + # of ways to win with a "10"] all divided by total number of possible hands

Answer 26

I HAVE NO CLUE ABOUT CARD GAMES..IT IS CONFUSING ME SO MUCH TO INTERPRET.

Answer 27

as Mikael showed, the # of ways to win with odds are 5*4*3 = 60

and the ways to win with a 10 are 9*8 = 72

So there are 60 + 72 = 132 winning hands

And there are 10*9*8 = 720 possible hands

So chance of winning is 132 / 720

Answer 28

The way you get the 5*4*3 is this:

How many odds in a 10 card deck where the cards are just numbered "1, 2, 3, etc"
Answer: 5 at first... but then you still draw 2 more cards.

So 5 odds are possible for the first card, and for each of those, there are 4 remaining odds in the mini-deck. On the third card, there are only 3 remaining odds left.
(say for example you drew a 7 first, then a 3, then a 1)

Answer 29

5 odds x 4 odds x 3 odds = 60 hands that are all odds

Answer 30

JAKEV8! I GOT THE FEEDBACK FROM MY ANSWER FOR WINNING HANDS 132 AS WRONG...NEED TO EVALUATE WHY?

Answer 31

HERE WINNING IS...ONE OF CARD IS 10 OR IF ALL OF CARDS ARE ODD... DO NOT UNDERSTAND THIS TWIST

Answer 32

PLEASE SOME ONE HELP ME. AM CONFUSED

Answer 33

3/10+5/10*4/9*3/8

Answer 34

276/720

Answer 35

Here is the correct Formula for this problem..Hope this helps
5*4*3=60
10=1*9*8+9*1*8+9*8*1=3*9*8=216
10=0
Winning Hands=276
# of Hands=10*9*8=720
Probability of winning=276/720

Answer 36

this answer proves correct