# Math

Here's a chalenging one that i can't do at all.

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

1. 👍 0
2. 👎 0
3. 👁 83

## Similar Questions

1. ### Math

A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are drawn from the deck and replaced each time back

asked by Alex on September 27, 2013
2. ### probability

Consider a deck of 52 cards with the following characteristics: 13 red cards, numbered 1 through 13 13 blue cards, numbered 1 through 13 13 green cards, numbered 1 through 13 13 black cards, numbered 1 through 13 1. Describe the

asked by wendell on June 18, 2012
3. ### Probability

Consider a deck of 52 cards with the following characteristics: 13 red cards, numbered 1 through 13 13 blue cards, numbered 1 through 13 13 green cards, numbered 1 through 13 13 black cards, numbered 1 through 13 1. Describe the

asked by Dina on October 13, 2012
4. ### math

A standard deck of cards has 52 cards in it. The cards are divided into 4 suits or 13 cards each.If one draws two cards at random from the deck of cards what is the probability that they are of the same suit ?

asked by Jason on July 16, 2017
5. ### math

A standard deck of cards has 52 cards in it. The cards are divided into 4 suits or 13 cards each.If one draws two cards at random from the deck of cards what is the probability that they are of the same suit ?

asked by Tim on July 11, 2017
6. ### Math Probabilities

A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are pulled in order from this deck of 52 playing cards.

asked by Alex on September 29, 2013
7. ### Math

A standard deck of cards is made up of four suits with 13 cards in each suit (total of 52 cards). If we randomly sample five cards from a standard poker deck, find the probability that all five cards selected are clubs.

asked by Jaime on June 21, 2010
8. ### Math (Probability)

A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are pulled in order, without replacement from this deck

asked by Alex on February 19, 2015
9. ### Math

A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Four cards are pulled in order from this deck of 52 playing

asked by Alex on February 19, 2015
10. ### math

A standard deck of playing cards had 52 cards. These cards are divided into four 13 card suits: diamonds, hearts, clubs, and spades. Find the probability of drawing a heart or a club at random from a deck of shuffled cards.

asked by Anonymous on March 9, 2016

More Similar Questions