SOLUTION: (1 pt) A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. (a) The card drawn is 9. The probability is: (b) The card drawn is

Click here to see ALL problems on Proportions

Question 393208: (1 pt) A card is drawn randomly from a standard 52-card deck. Find the probability of the given event.
(a) The card drawn is 9.
The probability is:
(b) The card drawn is a face card.
The probability is:
(c) The card drawn is not a face card.
The probability is:

---------------------------
(1 pt) 4 cards are drawn at random from a standard deck.
Find the probability that all the cards are hearts.
Find the probability that all the cards are face cards.
Note: Face cards are kings, queens, and jacks.
Find the probability that all the cards are even.
(Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13)

Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
card is drawn randomly from a standard 52-card deck
P(9 drawn) = 4/52
P(face card drawn) = 12/52
P(not a face card drawn) = 1 - 12/52
Present as You wish, fraction(lowest terms), decimal or percentage format
4 cards are drawn at random from a standard deck.
WILL ASSUME NON REPLACEMENT
p(all hearts) = (13/52)*(12/51)*(11*50)*(10*49)
P(all face cards)= (12/52)*(11/51)*(10/50)*(9/49)
P(all are even)=
will leave the counting of the number of even cards in the deck up to You

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The probability of anything is the number of ways that it can happen that you would consider a success divided by the number of ways it can happen total -- successes and failures.

There are 52 cards in the deck. 4 of them are 9s.

12 of them are face cards.

40 of them are not face cards. (or just subtract the answer to the previous question from 1)

The probability of successes in trials where is the probability of success on any given trial is given by:

Where is the number of combinations of things taken at a time and is calculated by

So for 4 hearts out of 4 cards dealt: , , and

So for 4 face cards out of 4 cards dealt: , , and

And for 4 even numbered cards out of 4 cards dealt: , , and

You get to do your own arithmetic. Hint: and

John

My calculator said it, I believe it, that settles it