You draw 2 cards from a well-shuffled deck of 52 cards. After you draw the first card, you do not replace it in the deck. What is the probability of P(get ace of spades on first draw and get queen of hearts on second draw)?

Question

anonymous · Answer

Firstly find the probability of  getting ace of spades..

How many ace of spades are there in 52 cards can you tell me ??

anonymous · Answer

As there is one ace of spades so probability will be:

$$P(Ace) = \frac{1}{52}$$

anonymous · Answer

Now this card is not replaced in that deck..

So now there are 51 cards in the deck and not 52..

Now, find the probability of selecting queen of Hearts there in the 51 cards:

As there is one queen of Hearts:

$$P(Queen) = \frac{1}{51}$$

anonymous · Answer

Now you have to just multiply them:

$$P(Ace \; \And \; Queen) = \frac{1}{52} \times \frac{1}{51} \implies \color{green}{\frac{1}{2652}}$$