If `Ma n dN` are any two events , teh probability that exactly one of them occur is a.`P(M)+P(N)-2P(MnnN)` b. `P(M)+P(N)-P(MnnN)` c.`P(M^c)+P(N^c)-2P(M^cnnN^c)` d. `P(MnnN^c)+P(M^cnnN)`

If Aa n dB are two events, the probability that exactly one of them occurs is given by a. P(A)+P(B)-2P(AnnB) b. P(Ann B )+P( A nnB) c. P(AuuB)-P(AnnB) d. P( A )+P( B )-2P( A nn B )

Aa n dB are two independent events. C is event in which exactly one of AorB occurs. Prove that P(C)geqP(AuuB)P(AnnB)dot

If A and B are any two events such that P(A) + P(B) -P(A and B) = P(A), then

The following Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections. Determine (a) P(A) (b) P(B nn barC) (c ) P(A uu B) (d) P(A nn barB) (e) P(B nn C) (f) Probability of the event that exactly one of A, B, and C occurs.

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is

If A, B, C are three events associated with a random experiment, prove that P(A uu B uu C) = P(A) + P(B) + P(C) - P(A nn B) - P(A nn C) P(B nn C) + P (A nn B nn C)

For the three events A ,B ,a n dC ,P (exactly one of the events AorB occurs) =P (exactly one of the two evens BorC ) =P (exactly one of the events CorA occurs) =pa n dP (all the three events occur simultaneously) =p^2w h e r e 0 < p < 1//2. Then the probability of at least one of the three events A ,Ba n dC occurring is a. (3p+2p^2)/2 b. (p+3p^2)/4 c. (p+3p^2)/2 d. (3p+2p^2)/4

It is tossed n times. Let P_n denote the probability that no two (or more) consecutive heads occur. Prove that P_1 = 1,P_2 = 1 - p^2 and P_n= (1 - P) P_(n-1) + p(1 - P) P_(n-2) for all n leq 3 .

If Aa n dB are events such that P(AuuB)=3//4.P(AnnB)=1//4,a n dP(A^c)=2//3 , then find (i) P(A) (ii) P(B) (iii) P(AnnB^c) (iv) P(A^cnnB)

Let E^c denote the complement of an event E. Let E,F,G be pairwise independent events with P(G) gt 0 and P(E nn F nn G)=0 Then P(E^c nn F^c nn G) equals (A) P(E^c)+P(F^c) (B) P(E^c)-P(F^c) (C) P(E^c)-P(F) (D) P(E)-P(F^c)