direct reasoning and indirect reasoning

Question

A standard deck of 52 cards consists of 4 suits. If a student deals 3 cards from a standard deck, determine the probability to the nearest hundredth, that at least one card is a heart. 

 

1. use the method direct reasoning

 

2. use the method indirect reasoning

Answer 1

I only saw your question today.

 

there are 13 hearts in a standard deck of 52 cards

 

if 3 cards are dealt, then the chance that card 1 will be heart will be 13/52 = .25 = 25% or 1 in 4

 

if card 1 is not a heart, then the chance that card 2 will be a heart will be 13/51 = 0.255 or 25.5% or 1 in 3.9

 

if cards 1 and 2 are NOT hearts, then the chance that card 3 will be a heart will be 13/50 = 0.26 = 26% or 1 in 3.8

 

if card 1 or card 2 is a heart, then the chance that card 3 will be a heart will be 12/51

 

if both cards 1 and 2 are hearts, then the chance that card 3 will be a heart will be 11/50

 

I apologize, but I cannot think of any way to answer this problem using indirect reasoning