Two cards are drawn from a deck of 52 plating cards. find the probability of each of the following events occurring:
a) both cards are clubs
b) both cards are red
c) both cards are queens
d) both cards are red queens
e) both cards are queens or both cards are red
a) 13 clubs out of 52 = 13/52
there will be 12 clubs left after picking the first one so: 12/52
so, (13/52)x(12/52) = 156/2704 chances to have both cards as clubs? is this correct?
b) (26/52)x(23/52) = 650/2704
C) (4/52)x(3/52) = 12/2704
d) (26/52)x(23/52) = 2/2704
how would i do e?
in making these calculations, you are replacing the first card.
This is incorrect as you are choosing 2 from 52,
hence after picking the first card, you have 51 left.
Therefore redo parts a), b) and c).
In part d), you must count the number of red queens.
For part e),
You can calculate the probabilities of getting 2 red cards and add to the probability of getting 2 queens....
but you must subtract the probability of getting 2 red queens as this is a conditional probability question. They will have already been accounted for.
There is overlap since some queens are red.
You only need to know how a pack is organised.
There are 26 red and 26 black.
There are 4 queens, 2 are red and 2 are black.
Therefore 2 of the 26 red cards are red queens.
Therefore there are 24 red cards that are not queens.
There are another 2 queens which are black.
If both cards are queens or both are red, then we must include the probability of also getting 2 black queens.
Also, the queens can be a black and red.
However if we include the 2 red queens, we must be aware that these are already counted,
since the 2 red queens have been already included in 2 red cards total.
Hence we can add the probabilities of 2 red cards to the probability of getting 2 queens,
but we must subtract the probability of getting 2 red queens.