Question

Two cards are drawn at random from a fack of 52 cards.What is the probability that either both are black or both are queen

Answer 1

both black

$= \binom{26}{2} = \frac{26 \times 25}{2} = 325$

both queens

$\binom{4}{2} = 6$

both black queens =

$\binom{2}{2} = 1$

probability that either both black or both queens =

$\frac{ 325 + 6 - 1}{ \binom{52}{2} }$

$\frac{330}{ \frac{52 \times 51}{2} }$

$\frac{330}{26 \times 51}$

$\frac{165}{13 \times 51}$

$\frac{55}{13 \times 17}$

$\frac{55}{221}$