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