Hi
Compute p(A), p(B), p(C), p(A and B) ...
and show that p(A and B)=p(A).p(B)
hai...stuck ..it simple but i still stuck. hope some one give me guide line how to solve
Question:
A coin is tossed three times. A is the event ' at least two tails' , B isthe event 'three heads or three tails, C is the event 'at least one tail. Which of the following are independent?
(a) A and B
(b) A and C
(c) B and C
solution:
(a) yes
(b) no
(c) no
so how to prove the ans
My outcomes as below:
HHH,HHT,HTH,HTT,THH,THT,TTH,TTT
Question (a)
i can calculate P(A) = P(HTT) = 1/2 * 1/2 * 1/2 = 1/8
= P(THT) = 1/2 * 1/2 * 1/2 = 1/8
= P(TTH) = 1/2 * 1/2 * 1/2 = 1/8
= P(TTT) = 1/2 * 1/2 * 1/2 = 1/8
There for P(A) = P(HTT) + P(THT) + P(TTH) + P(TTT)
= 1/8 + 1/8 + 1/8 + 1/8
= 4/8
= 1/2
is it correct P(A) = 1/2????
P(B) = P(HHH) + P(TTT)
= 1/8 + 1/8
= 1/4
p(A and B)= P (TTT) + P (TTT)
= 1/8 + 1/8
= 1/4
So, p(A and B) = P(A) * P(B)
1/4 = 1/2 * 1/4
= 1/8
so, not independent but the ans is independent