Question

What’s the chance of drawing a red card, followed by a queen of diamonds if I don’t put the first card back (in a shuffled deck of cards)?

Answer 1

In a shuffled deck of cards, there are 52 cards.

Now, the two cards are drawn without replacement.

This can be done in 52*51 ways; the first card can be drawn in 52 ways, and as the drawing is done without replacement, so the second card can be drawn in 51 ways.

So, the number of all possible cases is 52*51.

Now, we have to find the probability that a red card is drawn, followed by a queen of diamonds.

Now, there is only 1 queen of diamonds. That can be drawn in only 1 way.

Now, as there are only 26 red cards in the deck, when the queen of diamonds is drawn, there are only 25 left.

So, the red card can be drawn in 25 ways.

So, the required probability is

So, the probability of drawing a red card, followed by a queen of diamonds is 0.0094.