If P is a probability function, show that for any two events A, B. `P(AnnB)<= P(A)<=P(AuuB)<= P(A) +P(B)`

If P is a probability function, then show that for any two events A and B. P(AcapB)leP(A)leP(AcupB)leP(A)+P(B)

If P(A) and P(B) are the probabilities of occurrence of two events A and B, then the probability that exactly one of the two events occur, is

If A and B are two events then show that (i) (P(AnnB^(c)))=P(A)-P(AnnB) (ii) The probability that exactly one of them occurs is given by P(A)+P(B)-2P(AnnB)

If A and B 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( AnnB') c. P(AuuB)-P(AnnB) d. P( A' )+P( B' )-2P( A' nn B' )

Figure shows three events A ,B ,C and also the probabilities of the various intersections (for instance P(AnnB)=0. 07 ) determine P(A) (ii) P(Bnn C ) (iii) P(AnnB) (iv) P(Ann B ) (v) P(BnnC) (vi) probability of exactly one of the three events.

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 )

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

If A and B are two independent events, then show that the probability of occurrence of at least one of A and B is 1-P(A^')P(B^')

If 'P(A cup B)'='P(A cap B)' for any two events A and B ,then

If A and B are any two events such that P(A)=(2)/(5) and P(AnnB)=(3)/(20) , then the conditional probability, P(A//(A'uuB')) , where A' denotes the complement of A, is equal to