Probablity

Question

Answer 1

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.

Comments

I got same answer but key confused me

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Ya this wrong clearly..I have given you the proper justification

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I agree.