Thursday

April 17, 2014

April 17, 2014

Posted by **Jason** on Friday, March 9, 2007 at 4:02pm.

A deck of cards has 6 yellow, 6 green, and 5 black cards. You pick four cards from the deck. Cards are not returned after they are picked.

What's the probability of picking-

first not green, second not green, third not black, fourth not gray.

Its really hard.

Plz Help

You never mentioned gray cards. Do you mean the fourth card picked is not green? If not, ANY card drawn in not gray.

For the first draw, the not-green probability is 11/17. If this happens, there are 10 not-green cards left out of 16, and the probability of the second card being not green is 10/16. Now there are 15 cards left and 6 are green, since none were drawn. The other nine are either

4 yellow and 5 black, or

5 yellow and 4 black, or

6 yellow and 3 black

The relative probabilities of these situations are 3/11, 6/11 and 2/11, respectively. (I will leave you to figure out why).

The probability of the third card being not black is:

(3/11)(10/15) + (6/11)(11/15) + (2/11)(12/15) = (30+66+24)/165 = 120/165 = 8/11

The overall probability is

(11/17)*(5/8)*(8/11)* 1= 5/17

**Related Questions**

statistics - The red face cards and the black cards numbered 2-9 are put into a ...

math - A deck of cards has three yellow cards and five green cards. One green ...

Math - A standard deck of cards is made up of four suits with 13 cards in each ...

Probability - Consider a deck of 52 cards with the following characteristics: 13...

probability - Consider a deck of 52 cards with the following characteristics: 13...

Math - I am not sure how to go about figuring this out ... Shuffle the numbered ...

Math - Probability: There are 10 yellow cards, 6 green, 9 orange, and 5 red ...

math - A deck of 38 cards contains 16 blue cards, 6 red cards, and 16 yellow ...

Math - A standard deck of cards contains 52 cards. Of these cards there are 13 ...

math - A standard deck of cards has had all the face cards (Jacks, queens, and ...