`(i)` If the odds that the event `A` occurs is `5` to `7` find `P(A)`.
`(ii)` Suppose `P(B)=2/5`. Express the odds that the event B occurs.

{:(("i"), "The odds that the event A occurs is 5 or 7, find P(A)."),(("ii"), "Suppose P(B)" = 2/5. "Express the odds that the event B occurs."):}

The probability of event A is 3//4 . The probability of event B , given that event A occurs is 1//4 . The probability of event A , given that event B occurs is 2//3 . The probability that neither event occurs is

It is given that the events A and B are such that P(A) = 1/4, P (A//B) = 1/2 and P(B//A) = 2/3 . Then P(B) is

For three events A ,B and C ,P (Exactly one of A or B occurs) =P (Exactly one of B or C occurs) =P (Exactly one of C or A occurs) =1/4 and P (All the three events occur simultaneously) =1/16dot Then the probability that at least one of the events occurs, is :

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

If A and B are two events such that P(A uu B) = 0.7, P(A nn B) = 0.2, and P(B) = 0.5 , then show that A and B are independent.

The probability of an event A occur is 0.6 and B occuring is 0.3. If A and B are mutually exclusive events than the probability of neithetr A nor B occuring is :

The odds against a certain event are 5 to 2, and the odds in favor of another event independent of the former are 6 to 5. Find the chance that one at least of the events will happen.

Given that the events A and B are such that P(A) =(1)/(2) , P(AuuB) = (3)/(5) and P(B) = p. Find p if they are (i) mutually exclusive, (ii) independent.