aye

52 Cards

 

Suit \ Rank	Aces	Twos	Threes	Fours	Fives	Sixes	Sevens	Eights	Nines	Tens	Jacks	Queens	Kings
Heart	A	2	3	4	5	6	7	8	9	10	J	Q	K
Diamond	A	2	3	4	5	6	7	8	9	10	J	Q	K
Club	A	2	3	4	5	6	7	8	9	10	J	Q	K
Spade	A	2	3	4	5	6	7	8	9	10	J	Q	K

 

Number of red cards = \(13 \times 2 \\ = 26\)

Number of jacks = 4

 

 

⁵²P₂ = 2652 ways to get two cards.

 

Number of ways to get 2 red cards:

 

²⁶P₂ = 650 ways to get two red cards

 

Number of ways to get 2 jacks:

 

⁴P₂ = 12 ways

 

As the Jack of Hearts and Jack of Diamonds are considered two red cards, subtract one way.

 

We get 650 + 12 - 1 = 661 ways.

 

P(2 red card or 2 jacks) = \(661 \over 2652\)

                                      = 0.24925 (correct to 5 significant figures)

                                      = 24.925%

Hi MWizzard   :)

 

two cards are drawn from a standard deck of 52 cards. What is the probability that the following occurs? (2 red cards or 2 jacks)

 

 

P(2 reds OR 2jacks) = P(RR)+P(JJ)-P(2 red jacks)

 

\(=\frac{26}{52}\times \frac{25}{51}+\frac{4}{52}\times \frac{3}{51}-\frac{2}{52}\times\frac{1}{52}\\ =\frac{26*25}{52*51}+\frac{4*3}{52*51}-\frac{2*1}{52*51}\\ =\frac{650+12-2}{52*51}\\ =\frac{660}{2652}\\ =\frac{55}{221}\)

 

MWizzard, your answer is slightly wrong.  

These are all permutations and you can choose jack of hearts then jack of diamonds or vise versa. So that is 2 ways.

So you have to subtract 2 not 1.