Find the probability of selecting both red cards when 2cards are drawn (w/o replacement) from a standrd deck?

Find the probability of drawing a heart or a club from a standard deck of cards.





Find the probability of getting a three first and then a four when the die is rolled twice.





Find the probability of drawing a heart or a face card from a standard deck of cards.





Find the odds in favor of rolling the same number on a pair of dice.





Find the probability of drawing an ace and a jack when two cards are drawn (without replacement) from a standard deck of cards





Find the probability of drawing a heart or a black card from a standard deck of cards.

Find the probability of selecting both red cards when 2cards are drawn (w/o replacement) from a standrd deck?
1) First card = 26/52, second card = 25/51, thus


(26*25)/(52*51)





2) Heart = 13/52 or Club = 13/52, so (13/52) + (13/52) = 1/2





3) Pr(3)*Pr(4) = (1/6)(1/6) = 1/36





4) Pr(Heart) + Pr(Face) - Pr(Heart and Face) = (13/52) +(12/52) - (3/52) = 22/52 = 11/26





5) Pr(Any pip)Pr(Same pip) = (1)(1/6) = 1/6;


Odds = Favorable/Unfavorable = 1/5





6) Pr(Ace)Pr(Jack) + Pr(Jack)Pr(Ace) = 2(4/52)(4/51) = 8/663





7) Pr(Heart) +Pr(Black) =(13/52) + (26/52) = 3/4
Reply:1) 26/52 x 25/51


2) 26/52


3) 1/6 x 1/6


4) 25/52


5)1/6 x 1/6


6) 4/52 x 4/51


7) 39/52





Need to reduce the fractions, but you get the idea
Reply:1) 26/52 * 25/51, since there is once less red card and one less card in the deck.


2) 1/2, since half of the cards are hearts or clubs.


3) 1/6 * 1/6, since there is an equal chance of rolling a single number on any die roll.


4) 22/52, since there are 22 cards which are either hearts or face cards (J,Q,K of hearts are both hearts and face cards, so don't count them twice).


5) 1/1 * 1/6, since it doesn't matter what is on one die and the other die has a one in six chance of matching the first.


6) 4/52 * 4/51


7) 1/4 + 1/2