Yes.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)
C (13,2) = 78
P(E) = 78/1326
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 .
b) Both cards are red (3 marks)
(36, 2) = 630
P (E) = 630/1326
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:
c) Both cards are queens (3 marks)
(4,2) = 6
P(E) = 6/1326
Therefore, the probability that both cards are queens is 1/221
4 Queens. So 4/52 chance at first. Then 3/51. Total probability . You are correct here.
d) Both cards are red queens (3 marks)
(2,2) = 1
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
P(E) = 84/1326
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