e

Three coins are tossed. Events E_1, E_2, E_3 and E_4 are defined as follows. E_1 : Occurrence of at least two heads. E_2 : Occurrence of at least two tails. E_3 Occurrence of at most one head. E_4 : Occurrence of two heads. Describe the sample space and events E_1,E_2,E_3 and E_4 . Find E_1uuE_4,E'_3 . Also check whether E_2 and E_3 are equal.

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=j and vec e_idot vec E_j=0a n difi!=j , then prove that [ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=ja n d vec e_idot vec E_j=0a n difi!=j , then prove that [ vec e_1 vec e_2 vec e_3][ vec E_1 vec E_2 vec E_3]=1.

If vec e_(1),vec e_(2),vec e_(3) and vec E_(1),vec E_(2),vec E_(3) are two sets of vectors such that vec e_(i)*vec E_(j)=1, if i=j and vec e_(i)*vec E_(j)=0 and if i!=j then prove that [vec e_(1)vec e_(2)vec e_(3)][vec E_(1)vec E_(2)vec E_(3)]=1

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=ja n d vec e_idot vec E_j=0a n difi!=j , then prove that [ vec e_1 vec e_2 vec e_3][ vec E_1 vec E_2 vec E_3]=1.

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=j and vec e_idot vec E_j=0a n difi!=j , then prove that [ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.