SOLUTION: 1. A card is drawn from an ordinary deck and we are told that it is red, what is the probability that the card is greater than 2 but less than 9?

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Question 427342: 1. A card is drawn from an ordinary deck and we are told that it is red, what is the probability that the card is greater than 2 but less than 9?
Found 2 solutions by sudhanshu_kmr, Edwin McCravy:
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

total no. of red cards = 26
total no. of red cards greater than 2 but less than 9 = 12

probability = 12/26
= 6/13

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1. A card is drawn from an ordinary deck and we are told that it is red, what is the probability that the card is greater than 2 but less than 9? 


Here is a complete deck of 52 cards:
 

A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ 
A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦
A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  
A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ 
 
We are told that the card is red, so we can remove all the 
black cards and have only this smaller deck of 26 red cards:


A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ 
A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦
 


So we want the probabilty that out of those 26 red cards, 
the card that is drawn is one of these 12:


          3♥   4♥   5♥   6♥   7♥   8♥   
          3♦   4♦   5♦   6♦   7♦   8♦
 


So the desired probability is 12 out of 26, or 12/26 
which reduces to 6/13.

Edwin