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Consider an ordinary deck of 52 cards. In this deck, there are 4 suits and 2 col

ID: 3151667 • Letter: C

Question

Consider an ordinary deck of 52 cards. In this deck, there are 4 suits and 2 colors: 13 diamonds and 13 hearts (both red) and 13 clubs and 13 spades (both black). Within each suit, the 13 cards labeled as 2,3,4,5,6,7,8,9,10,jack,queen,king, and ace.

Suppose you are drawing a single card at random from this deck. Find the following probabilities. You may enter your answer as either a fraction or a decimal.

a. P(heart)=  
b. P(red)=  
c. P(queen)=  
d. P(heart | queen)=  
e. P(heart | red)=  
f. P(queen | red)=  

g. Based on the above calculations, we can conclude that the events "draw a heart" and "draw a red" are  ---Select---  dependent or independent

h. Based on the above calculations, we can conclude that the events "draw a queen" and "draw a red" are  ---Select---  independent or dependent

i. Based on the above calculations, we can conclude that the events "draw a heart" and "draw a queen" are  ---Select--- dependent or independent

Explanation / Answer

a. P(heart)= 13/52 = 1/4
b. P(red) = 26/52 = 1/2
c. P(queen)= 4/52 = 1/13
d. P(heart | queen)= P(Heart AND Queen)/P(Queen) = (1/52)/(4/52) = 1/4
e. P(heart | red)= P(Heart AND Red)/P(Red) = (13/52)/(26/52) = 1/2
f. P(queen | red)= P(Queen AND Red)/P(Red) = (2/52)/(26/52) = 1/13

g. Based on the above calculations, we can conclude that the events "draw a heart" and "draw a red" are : Dependent

h. Based on the above calculations, we can conclude that the events "draw a queen" and "draw a red" are : Independent

i. Based on the above calculations, we can conclude that the events "draw a heart" and "draw a queen" are : Independent