Compute the probability that a hand of 13 cards contains:

a) the ace and king of at least one suit.

b) all 4 of at least 1 of the 13 denominations.

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- Sep 16th 2009, 01:39 PMcgiulz13 card hand
Compute the probability that a hand of 13 cards contains:

a) the ace and king of at least one suit.

b) all 4 of at least 1 of the 13 denominations. - Sep 16th 2009, 02:58 PMPlato
Suppose that $\displaystyle \mathcal{S}$ is the event that the hand contains the ace and king of spades.

Then $\displaystyle P(\mathcal{S})=\frac{\binom{50}{11}}{\binom{52}{13 }}$.

Now you want to find $\displaystyle P(\mathcal{S}\cup\mathcal{H}\cup \mathcal{C}\cup \mathcal{D})$.