Three player `A, B and C`, toss a coin cyclically in that order (that is `A, B, C, A, B, C, A, B,...`) till a headshows. Let p be the probability that the coin shows a head. Let `alpha, beta and gamma` be, respectively, theprobabilities that `A, B and C` gets the first head. Then

Show that if A ⊂ B , then C – B ⊂ C – A .

A certain coin is tossed with probability of showing head being 'p' . Let 'q' denotes the probability that when the coin is tossed four times the number of heads obtained is even. Then

In a relay race there are five terms A, B, C, D and E. (a) What is the probability that A, B and C finish first, second and third, respectively. (ii) What is the probability that A, B and C are first three to finish (In any order) (Assume that all finishing orders are equally likely).

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (a-b)r+(b-c)p+(c-a)q=0

Probability that A speaks truth is 4/5 . A coin is tossed. A reports that a head appears. The probability that actually there was head is (A) 4/5 (B) 1/2 (C) 1/5 (D) 2/5

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

An unbiased coin is tossed 6 times. The probability that third head appears on the sixth trial is a. 5//16 b. 5//32 c. 5//8 d. 5//64

Show that the points (a,b+c) (b,c+a) and (c,a+b) are collinear.

Show that points A ( a,b +c) , B( b,c+a) , C( c,a+b) are collinear.