220 views P(A and B get same number of heads) = P(A and  B both get 0 head ) + P(A and B both get 1 head) +  P(A and B both get 1 head) +  P(A and B both get 1 head)                                      .................(1)

Now P(A and  B both get 0 head ) :   3C0 (1/2)3 . 3C0 (1/2)3 [Since A and B toss 3 coins each separately so they need to be considered separate events.Also since it is a coin toss problem so it considers the requirements of binomial distribution and hence we apply this formula but separately for A and B and multiplying them since both of them will occur hence follows multiplication principle and also A and B are separate events as mentioned earlier]

=  1/64

SImilarly P(A and  B both get 1 head ) :  3C1 (1/2)3 . 3C1 (1/2)3

=  9/64

SImilarly P(A and  B both get 2 heads ) :  3C2 (1/2)3 . 3C2 (1/2)3

=  9/64

SImilarly P(A and  B both get 3 heads) :  3C3 (1/2)3 . 3C3 (1/2)3

=  1/64

Hence from (1) , we have :

P(A and B get same number of heads)  =  1/64 + 9/64 + 9/64 + 1/64

= 20/64

=  5/16

Hence , C) should be the correct option.

I got same answer but key confused me Ya this wrong clearly..I have given you the proper justification
I agree.