Probability 4

Question

A card is drawn from a well shuffled deck of 52 cards. Find the probability that the card is a red card or a 3.

Answer 1

Think of it like a Venn Diagram. 
1/2 the deck is red. 
1/13th of the deck is a 3. 

You can't just ADD 1/2 + 1/13th b/c that would be double counting the cards that are both RED and 3. which there are 2 of.  

 

The "strict" math method would be 1/2 + 1/13th - 1/26   (Red + 3s - overlap)   = 7/13 
The easiest way is to recognize 1/2 + 1/26 (That's ALL Reds [including 2 red 3's] + the 2 BLACK 3's) = 7/13

Answer 2

There are 26 red cards in a deck of 52 cards, 13 hearts and 13 diamonds.

The probability of picking a red card is 26/52. However, in this group of 26 cards there is the 3 of hearts and the 3 of diamonds. Therefore the probability of picking a 3 is only 2/52 and not 4/52 because the probability of picking a red 3 is included in the 26/52.

P=26/52+2/52=28/52=7/13.