Question

What is the probability that 2 cards selected from a standard deck of 52 cards without replacement are both multiples of 2?

Answer 1

so we can say

P(multiple of 2 | multiple of 2)

well, the deck has 52 cards, every other card is an even card and thus a multiple of 2, so we can say 26 of 52 are multiple of 2, so

P(multiple of 2) = 0.5 or 1/2

what are the chances the next one is also multiple of 2?

well, we need both probabilities to be true, so we can and is an AND case and in an AND that means multiplication or

P(multiple of 2) * P(multiple of 2)

but there's no replacement, so for our second card, we no longer have 52 in the deck, we only have 51 and we no longer have 26 even ones, one came out, so we only have 25, so

`P(\textit{multiple of 2} ~~ | ~~ \textit{multiple of 2})\implies \stackrel{ \textit{1st card} }{P(\textit{multiple of 2})} * \stackrel{ \textit{2nd card} }{P(\textit{multiple of 2})} \\\\\\ \stackrel{ \textit{1st card} }{\cfrac{26}{52}}* \stackrel{ \textit{2nd card} }{\cfrac{25}{51}}\implies \cfrac{1}{2}* \cfrac{25}{51}\implies \cfrac{25}{102}\approx 0.2451\approx 25\%`