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
b) Both cards are red
c) Both cards are queens
d) Both cards are red queens

Can you show me the formula and also show me the step by step procedure .
Thank you

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Originally Posted by rickjosh19

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

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a) Both cards are clubs

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Think about it. These are pretty basic probability problems.

How many clubs are in a deck? 13. The prob of drawing the first is 13/52.

Assuming no replacement, there are 51 cards and 12 clubs left after drawing the first. So, the prob. Is 12/51

(13/52)(12/51)=1/17. See? Now, you try the others and lets see your progress. OK?

For b, how many red cards are there? You have hearts and diamonds.

c, How many queens are in a deck?

d, How many red queens?

Do these as I done the first and you'll be OK.

a) N(S) = C(52, 2)
= 1326

The number of ways of choosing 2 clubs is C (13, 2)

C (13, 2) = 78

P (E) = 78/1326

= 1/17

The probability of choosing both clubs being clubs is 1/17