## What is the probability of drawing a red card and then drawing a spade without replacing the card that was drawn first

Question

What is the probability of drawing a red card and then drawing a spade without replacing the card that was drawn first

in progress 0
8 mins 2021-10-13T05:47:31+00:00 1 Answer 0

13/102

Step-by-step explanation:

There are 52 cards in a standard deck (not including the jokers).

So let’s start with the first thing… the red part. Half the deck is red which means 52/2=26 cards are red.

So the probability of the red being drawn is 26/52 (I’m going to keep it an un-reduced form for now)

So now since it says we don’t replace (we don’t put the card back into the deck), there is only 51 cards to choose from now.  There are 4 suits so there are 13 of each kind of suit. So to draw a spade, the probability would be 13/51.

So the end: The probability of drawing a red then a spade without replacing is the multiplication of these probabilities I found:

So the answer is 26/52  * 13/51=13/102