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**cnmath16** Q. **Two cards are drawn from a deck of 52 playing cards. Find the probability of each of the following events occurring:**

a) Both cards are clubs (3 marks)

N(S) = (52,2)

= 1326

C (13,2) = 78

P(E) = 78/1326

=39/663

=13/221

Therefore the probability that both cards are clubs is 13/221

**You have a 1 in 4 chance of picking a club to start with. Once you have picked a club, then there are 51 cards left in the pack, 12 of which are clubs. So you have a 12/51 chance. The odds of both occuring is $\displaystyle \frac{1}{4} \times \frac{12}{51} $.**

b) Both cards are red (3 marks)

(36, 2) = 630

P (E) = 630/1326

=315/663

=105/221

Therefore, the probability that both are red is 105/221.

**1/2 chance of picking a red card. Then there will be 25 red cards in a pack if 51. So chance of picking another one is 25/51. Total probability of both occuring: $\displaystyle \frac{1}{2} \times \frac{25}{51} $**

c) Both cards are queens (3 marks)

(4,2) = 6

P(E) = 6/1326

= 1/221

Therefore, the probability that both cards are queens is 1/221

** 4 Queens. So 4/52 chance at first. Then 3/51. Total probability $\displaystyle \frac{4}{52} \times \frac{3}{51}$. You are correct here. **

[b]

d) Both cards are red queens (3 marks)

(2,2) = 1

P(E)= 1/1326

Therefore, the probability that both are red queens is 1/221.

**2 red queens. Chance of the first being a red queen is 2/52. Chance of 2nd being a red queen is 1/51. Total probability 2/52 x 1/51 **

e) Both cards are queens or both cards are red.

(32,2) + (4,2)

= 78 + 6

= 84

P(E) = 84/1326

= 42/663

= 14/221

Therefore the probability that both cards are queens or both are red is 14/221.

** Just add b) and c)**

Please check and let me know if I am correct. THANK YOU