Draw one card at random from a standard deck of cards. The

Chapter 1, Problem 3E

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QUESTION:

Draw one card at random from a standard deck of cards. The sample space \(S\) is the collection of the 52 cards. Assume that the probability set function assigns \(1 / 52\) to each of the 52 outcomes. Let

             

              \(A = {x: x\) is a jack, queen, or king},

             

              \(B = {x: x\) is a 9, 10, or jack and x is red},

             

               \(C = {x: x\) is a club},

             

               \(D = {x: x\) is a diamond, a heart, or a spade}.

Find (a) \(P(A)\), (b) \(P(A \cap B)\), (c) \(P(A \cup B)\), (d) \(P(C \cup D)\), and (e) \(P(C \cap D)\).

Equation Transcription:

 

 

Text Transcription:

S  

1/52

A={x:x    

B={x:x  

C={x:x  

D={x:x    

P(A)  

P(A cap B)  

P(A cup B)  

P(C cup D)  

P(C cap D)

Questions & Answers

QUESTION:

Draw one card at random from a standard deck of cards. The sample space \(S\) is the collection of the 52 cards. Assume that the probability set function assigns \(1 / 52\) to each of the 52 outcomes. Let

             

              \(A = {x: x\) is a jack, queen, or king},

             

              \(B = {x: x\) is a 9, 10, or jack and x is red},

             

               \(C = {x: x\) is a club},

             

               \(D = {x: x\) is a diamond, a heart, or a spade}.

Find (a) \(P(A)\), (b) \(P(A \cap B)\), (c) \(P(A \cup B)\), (d) \(P(C \cup D)\), and (e) \(P(C \cap D)\).

Equation Transcription:

 

 

Text Transcription:

S  

1/52

A={x:x    

B={x:x  

C={x:x  

D={x:x    

P(A)  

P(A cap B)  

P(A cup B)  

P(C cup D)  

P(C cap D)

ANSWER:

Solution :

Step 1 :

Here the sample space S is a collection of 52 cards. And the probability of selecting each outcome is 1/52 . the events are defined as

A = { x: x is jack, queen or king}

B = { x: x is 9 ,10 or jack and x is red }

C = { x: x is club}

D  = { x : x is a heart, a diamond . or a spade }

We have to find

P(A), P(A,P(AP(C,and P(C.


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