Algebra/probability 2 help please!

Question

A card is drawn randomly from a standard 48-card pinochle deck. Find the probability of drawing the given card. (Note that a pinochle deck consists of all four suits. The cards 9, 10, jack, queen, king, ace appear twice in each suit. There are no 2, 3, 4, 5, 6, 7, or 8s.)



6. any ace

7. any black queen

8. any heart

9. any 9 or 10

10. any ace of hearts

11. any 7 

(Please show work!)

Thanks!

Answer 1

Please see video answer.

Correction, I thought any 7 cards for #11.

There are no "7" cards in deck, so probability is 0/48 = 0

Answer 2

When doing probability, you want to take the favorable outcome over all of the possible outcomes. So for number six you would take the amount of aces in the deck (8) divided by the total amount of cards in the deck (48). So your work will look something like this:

6. 8/48=1/6=16.67% There are 8 aces in this deck because there are 4 different suits and 2 aces for each suit.

7. 4/48=1/12=8.33% There are 2 suits that are black (clubs and spades) and there are 2 queens in each suit.

8. 12/48=1/4=25% There are 12 heart cards in this deck.

9. 16/48=1/3=33.33% There are 2 9s and 2 10s in each suit and there are 4 suits so there are 16 possible favorable outcomes.

10. 2/48=1/24=4.167% There are only 2 ace of hearts.

11. 0/48=0=0% There are no 7s in this deck so there are 0 favorable outcomes.

I hope this helps!

Answer 3

To find the probability of drawing a given card we simply need to count the number of times that card occurs in the deck and divide by the total number of cards (48).

6.) Since each suit appears twice and there are 4 suits, then the number of aces in the deck is 2*4 = 8. Thus,

P(any ace) = 8/48 = 1/6

7.) Since each suit appears twice and only 2 suits are black, the number of black queens is 2*2 = 4. So,

P(black queen) = 4/48 = 1/12

8.) Since each suit consists of only 6 unique cards, but each card appears twice, the total number of hearts in the deck is 6*2 = 12. Therefore,

P(any heart) = 12/48 = 1/4

9.) Since there are 4 suits and each suit has 2 of each card (in this case 9 and 10), the total number of 9s and 10s cards is 4*2*2 = 16. So,

P(any 9 or 10) = 16/48 = 1/3

10.) Since each suit has 2 of each card, there are 2 ace of hearts in the deck. Thus,

P(any ace of hearts) = 2/48 = 1/24

11.) Since there are no 7s present in the deck

P(any 7) = 0