Question

question: A fair coin is tossed 3 times. Show that the events “at least one head & at least one tail” and “heads on the 2nd toss” are independent

Answer 1

S = {hhh, hht, hth, htt, ttt, tth, tht, thh}

n(S) = 8

Let A = at least one head & at least one tail

A = {hht, hth, htt, tth, tht, thh}

n(A) = 6

P(A) = 6/8 = 3/4

Let B = heads on the 2nd toss

B = {hhh, hht, tht, thh}

n(B) = 4

P(B) = 4/8 = 1/2

A and B = {hht, tht, thh}

P(A and B) = 3/8

Now, P(A|B) = P(A and B)/P(B) = (3/8)/(1/2) = 3/4 = P(A)

This means A and B are independent events.