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
To find the probability of picking a specific sequence of cards, we can multiply the probabilities of each individual event. Let's break it down step-by-step:
1. First card: The probability of picking a card that is not green is 11/17. This is because there are 11 non-green cards (6 yellow + 5 black) out of a total of 17 cards.
2. Second card: Since the first card was not green, there are now 16 cards remaining, out of which 10 are not green. So, the probability of picking a second card that is not green is 10/16.
3. Third card: Now, the remaining cards in the deck consist of either 4 yellow and 5 black cards, or 5 yellow and 4 black cards, or 6 yellow and 3 black cards. The probabilities of these three scenarios are as follows:
- P(4 yellow and 5 black) = 3/11
- P(5 yellow and 4 black) = 6/11
- P(6 yellow and 3 black) = 2/11
The probability of picking a third card that is not black depends on which scenario occurred. In the first scenario, there are 10 non-black cards out of 15 remaining. In the second scenario, there are 11 non-black cards out of 15 remaining. In the third scenario, there are 12 non-black cards out of 15 remaining. Therefore, the probability can be calculated as follows:
- P(Third card not black) = (3/11)*(10/15) + (6/11)*(11/15) + (2/11)*(12/15) = 8/11
4. Fourth card: Based on your clarification, the fourth card can be any color (not necessarily gray). Therefore, the probability is 1.
Finally, we multiply all the probabilities together to find the overall probability:
(11/17)*(10/16)*(8/11)*(1) = 5/17
So, the probability of picking a sequence where the first card is not green, the second card is not green, the third card is not black, and the fourth card is not gray is 5/17.