Q1 A fair coin is tossed three times Consider the following

Q1 : A fair coin is tossed three times. Consider the following events:

A:Heads on the first toss

B:Tails on the second toss

C:All three outcomes the same (HHH or TTT)

(a) Which of the following pairs of these events are independent? Give a brief explanation for each of your answers, and show all work

(1)A,B

(2)A,C

(3)B,C

(b) Are the three events independent? Again, give a brief explanation for your answer, and show all work

Solution

a) A and B are independent...

P(A) = 0.5 P(B) = 0.5 P(C) = (0.5)^3 + (0.5)^3 P(D) = 0.5 X (0.5)^2 P(AB) = 0.5 X 0.5 P(ABC) = 0 P(ABD) = (0.5) X (0.5)^2 --------------------------------------------------- P(AB) = P(A) P(B) Hence A and B are independent. P(ABC) =! P(A)P(B)P(C) Hence A,B and C are not independent. P(ABD) =! P(A)P(B)P(D) Hence A,B and D are not independent. ---------------------------------------------------------------------------------- Please rate Thanks.