A fair coin is tossed two times, and the events A and B are defined as shown bel

Question

A fair coin is tossed two times, and the events A and B are defined as shown below. Complete parts a through d. A: {At least one head is observed} B: {The number of heads observed is odd} a. Identify the sample points in the events A, B, A Union B, A^c, and A Intersection B. Identify the sample points in the event A. Choose the correct answer below. A. A: {TH, HT} B. A {TT} C. A: {TH, HT, HH} D. There are no sample points in the event. Identify the sample points in the event B. Choose the correct answer below. A. B: {TH, HT, HH} B. B: {TT} C. B: {TH, HT} D. There are no sample points in the event. Identify the sample points in the event A Union B. Choose the correct answer below. A. A Union B: {TH, HT} B. A Union B: {TH, HT, HH} C. A Union B: {TT} D. There are no sample points in the event. Identify the sample points in the event A^c. Choose the correct answer below. A. A^c: {TH, HT, HH} B. A^c: {TT} C. A^c: {HH} D. There are no sample points in the event. Identify the sample points in the event A Intersection B. Choose the correct answer below.

Explanation / Answer

Given

A fair coin is tossed 2 times

A - {atleast one head is observed }

B-{ the number of heads observed is odd}

the sample sapce for event A = [ {(HH)},{(HT)},{(TH)}, {(HT) , (TH)} , {(HT) , (HH)} {(HH) , (TH)} {(HT) ,(TH) ,(HT)}

the sample space of B = [ (HH)},{(HT)},{(TH)} ,   {(HT) ,(TH) ,(HT)} ]

now looking at the sample space we can solve the question

A)identify the sample space and choose the correct answer below ?

options A and C are correct

by observing the sample space we came to know {(HT) , (TH)} , {(HT) ,(TH) ,(HT)} both are present in the sample space

B)identify the sample points in B ?

Option a is correct once obseve the sample space of B  {(HT) ,(TH) ,(HT)} is the only option in the given options

C) sample points in (A U B)

Option A and B are correct

the sample sapce for event A = [ {(HH)},{(HT)},{(TH)}, {(HT) , (TH)} , {(HT) , (HH)} {(HH) , (TH)}   {(HT) ,(TH) ,(HT)}

the sample space of B = [ (HH)},{(HT)},{(TH)} ,   {(HT) ,(TH) ,(HT)} ]

both A and B are present in the sample sapce

d) Ac   ?

Ac we should not have head in the sample point that is {(TT)}

hence option B is correct

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