Q.4   A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.

Answers (1)
S seema garhwal

 A fair coin and an unbiased die are tossed,then total outputs are:

                       = \left \{ (H1),(H2),(H3),(H4),(H5),(H6),(T1),(T2),(T3),(T4),(T5),(T6) \right \}

                      =12                                         

A is the event ‘head appears on the coin’ .

Total outcomes of A are : = \left \{ (H1),(H2),(H3),(H4),(H5),(H6) \right \}

                                                                              P(A)=\frac{6}{12}=\frac{1}{2}

 B is the event ‘3 on the die’.

Total outcomes of B are : = \left \{ (T3),(H3)\right \}

                                             P(B)=\frac{2}{12}=\frac{1}{6}

                       \therefore A\cap B = (H3)

                           P (A\cap B) = \frac{1}{12}

  Also,                P (A\cap B) = P(A).P(B) 

                         P (A\cap B) = \frac{1}{2}\times \frac{1}{6}=\frac{1}{12}

Hence, A and B are independent events.

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