Of three independent events, the chance that only the first occurs, is `a ,` the chance that only the second occurs if `b ,` and the chance of only the third is `cdot` Show that the chances of three events are, respectively, `a//(a+x),b//(b+x),c//(c+x)=x^2`

Of the three independent event E_(1),E_(2) and E_(3) , the probability that only E_(1) occurs is alpha , only E_(2) occurs is beta and only E_(3) occurs is gamma . If the probavvility p that none of events E_(1), E_(2) or E_(3) occurs satisfy the equations (alpha - 2beta)p = alpha beta and (beta - 3 gamma) p = 2 beta gamma . All the given probabilities are assumed to lie in the interval (0, 1). Then, ("probability of occurrence of " E_(1))/("probability of occurrence of " E_(3)) is equal to

Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is 194//285 b. 1//57 c. 13//19 d. 3//4

Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is 194//285 b. 1//57 c. 13//19 d. 3//4

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 :

If A ,B ,C be three mutually independent events, then Aa n dBuuC are also independent events. Statement 2: Two events Aa n dB are independent if and only if P(AnnB)=P(A)P(B)dot

Three coins are tossed once. Let A denote the event 'three heads show", B denote the event "two heads and one tail show", C denote the event" three tails show and D denote the event 'a head shows on the first coin". Which events are (i) mutually exclusive? (ii) simple (iii) Compound?